The Messenger of Allaah صلى الله عليه وسلم said, "Certainly, the one who will live among you will see lots of differences. So stick to my sunnah and the sunnah of the right-principled and rightly-guided successors. Bite onto that with your molar teeth." 
The Prophet صلى الله عليه وسلم mentioned his own sunnah and then mentioned the sunnah of his rightly-guided successors رضي الله عنهم. These successors are called raashideen because they know the truth and they judge or act in accordance with it. Raashid (راشد) is the opposite of ghaawa (غاوى). Ghaawa implies recognizing the truth but not following it. The Prophet صلى الله عليه وسلم also described them as mahdiyeen (المهديّين). This means that Allah has guided them to the truth and has not led them astray from it. This is the opposite of dhaal (ضال) or one who is astray from the truth and does not know the truth.
For these successors to be true examples for others to follow, it is a must that they had to have recognized the truth, were guided and followed it. Otherwise, they are not worthy of being followed.
Who are the "Rightly-Guided Successors"?
Most of the commentators on this hadith state that the term "rightly guided successors" is a reference to Abu Bakr, Umar, Uthmaan and Ali رضي الله عنهم, who were the leaders of the Muslim community after the death of the Prophet صلى الله عليه وسلم. The Prophet صلى الله عليه وسلم knew that they would follow his teachings and his way. Hence, he guided his followers to follow their path. The proof for that position is the hadith of the Prophet صلى الله عليه وسلم, "The successorship (khilaafah) will last for thirty years among my Nation and then there will be a kingship after that." 
When one adds up the terms of Abu Bakr, Umar, Uthmaan and Ali رضي الله عنهم, the total comes to thirty years. The khilaafah of Abu Bakr رضي الله عنه was for two years and three months, the khilaafah of ' Umar رضي الله عنه was for ten and a half years, the khilaafah of ' Uthmaan رضي الله عنه was for twelve years, the khilaafah of 'Ali رضي الله عنه was for four years and nine months. [At the end of this list, some also include the khilaafah of Imaam al-Hasan رضي الله عنه that lasted only six months.]
There are hadith that talk about the khilaafah in a more general sense, for they include other than the aforementioned Companions رضي الله عنهم. Those hadith make it clear that the khilaafah in general was for more than thirty years. Hence, these thirty years of these Companions رضي الله عنهم are something special in the sense of khilaafah. Their special aspect is that they were headed by the rightly guided successors as mentioned by the Prophet صلى الله عليه وسلم.
The opinion that the referred-to rightly-guided successors are Abu Bakr, Umar, Uthmaan and Ali رضي الله عنهم is the opinion of at-Tahaawi رحمه الله, an-Nawawi رحمه الله, ibn al-Arabi رحمه الله, ibn Daqeeq al-Eid رحمه الله, at-Teebi رحمه الله, al-Alaai رحمه الله, ibn Rajab رحمه الله, ibn Abu al-Izz رحمه الله, al-Mubaarakfoori رحمه الله, Suhaaranfoori رحمه الله, ar-Rasheed رحمه الله, as-Salmaan رحمه الله, al-Bugha and Mistu, and Sultaan. 
lbn al-Arabi رحمه الله, ibn Daqeeq al-Eid رحمه الله and Al-Alaai رحمه الله claim that there is a consensus on this point. Al-Haitami رحمه الله explicitly mentions the four and adds Imaam al-Hasan رضي الله عنه as the fifth. 
It should also be noted that of the four rightly-guided caliphs, Abu Bakr رضي الله عنه and Umar رضي الله عنه have a distinction apart from the other two. The Prophet صلى الله عليه وسلم enjoined Muslims to follow the ways (sunnah) of the right-principled caliphs, but he asked Muslims to specifically imitate only two of them, Abu Bakr رضي الله عنه and 'Umar رضي الله عنه. He said, "Imitate those two who come after me, Abu Bakr and Umar." 
There is a difference between following one's ways (ittiba sunnati-hi) and imitating him (iqtida bihi), which gives a greater weight to their acts. The status of Abu Bakr and 'Umar, then, is greater than the status of ' Uthmaan and Ali, may Allah be pleased with them all.
The Legal Status of the Four Rightly-Guided Caliphs رضي الله عنهم
If the Prophet صلى الله عليه وسلم ordered Muslims to stick to the path of the rightly-guided successors and assuming that such is in reference to Abu Bakr, Umar, Uthmaan and Ali رضي الله عنهم, what is the status of their rulings and opinions from a legal theory point of view? Does one have to follow their opinions and ijtihaad? If they all agree on a matter, does that mean that their agreement must be followed?
[There is a difference of opinion concerning the authority of the statement of a Companion of the Prophet صلى الله عليه وسلم in general. There are eight different views concerning that issue:
(1) The statement of a Companion is a proof and authority, unconditionally;
(2) The statement of a Companion is unconditionally not a proof or authority;
(3) The statement of the four caliphs only is a proof or authority;
(4) The statement of Abu Bakr or Umar only is an authority;
(5) The statement of the four caliphs and others similar to them in virtue only is an authority;
(6) The statement of the first three caliphs only is an authority;
(7) The statement of a Companion is an authority only if it is in agreement with analogy;
(8) The statement of a Companion is an authority only when it contradicts analogy.
See an-Namlah, vol. 4, pp. 274-275; also see al-Alaai, Ijmaal, passim. Obviously, those who say that the statement of any Companion is unconditionally an authority will have no problem in saying that the statement of any of the four rightly-guided caliphs is an authority.]
It is known that, in general, Umar رضي الله عنه would follow the practice of Abu Bakr رضي الله عنه. Similarly, Uthmaan رضي الله عنه would follow the practice of his two predecessors. Ali رضي الله عنه was also very careful in following the decrees of Umar رضي الله عنه. The later caliph Umar ibn Abdul Azeez رحمه الله said clearly that no one should stray from their paths. 
There is no doubt that the four rightly-guided caliphs رضي الله عنهم were very pious and very knowledgeable. Thus, their opinions should be highly respected and not taken lightly. The question here is whether or not one must or should follow their opinions as opposed to following the opinions of others, say of other Companions رضي الله عنهم, for example.
Al-Alaai رحمه الله points out that some people say that if the four caliphs رضي الله عنهم agree upon something, it is to be considered a consensus and it is not allowed for anyone to differ from that opinion. Al-Alaai رحمه الله states that such is not correct and he goes on to refute that particular view. 
An-Namlah رحمه الله points out that such cannot be considered a consensus if any of the other Companions رضي الله عنهم disagreed with them. However, if none of the other Companions رضي الله عنهم disagreed with the four caliphs رضي الله عنهم, then it is not a matter of the four caliphs رضي الله عنهم agreement being a consensus but it now becomes a matter of the consensus of the Companions رضي الله عنهم, which is a different issue. 
The Companions رضي الله عنهم themselves sometimes differed with the four caliphs رضي الله عنهم. Indeed, the four caliphs رضي الله عنهم sometimes differed from each other and did not always follow the opinions of their predecessors. 
This is a sign that the Companions رضي الله عنهم themselves did not consider the statements of the four caliphs رضي الله عنهم or of any of them as a final authority in Islamic law. Even those who would accept their statements as authority, based on this hadith, state that simply because their statement is an authority, it does not mean that it has the same rank as the sunnah of the Prophet صلى الله عليه وسلم himself. Not everything which is an authority in Islamic law is of the same status or strength. Hence, if there is any conflict between what any of these four caliphs رضي الله عنهم said and what the Prophet صلى الله عليه وسلم said or did, then the Prophet 's sunnah would definitely take precedence. 
The question is more related to cases where the four caliphs رضي الله عنهم did something that was not in contradiction to the Prophet's صلى الله عليه وسلم sunnah although it did not particularly form part of the Prophet's صلى الله عليه وسلم sunnah. In this case, is the statement or practice of the rightly-guided successors رضي الله عنهم necessary to be followed?
Many of the commentators on this hadith understand the guidance given here in a qualified or restricted sense. lbn al-Arabi رحمه الله and ibn Daqeeq al-Eid رحمه الله, for example, understood this hadith to mean that if a person is not a knowledgeable person, then, if he must blindly follow somebody else's opinion, he should follow the opinion of one of the four rightly-guided caliphs رضي الله عنهم. They state, furthermore, that if there is a difference of opinion among the Companions رضي الله عنهم, then more weight is to be given to the opinions of the four caliphs رضي الله عنهم, based on this hadith. 
Suhaaranfoori رحمه الله also says that this hadith is evidence that if one of the four rightly-guided caliphs رضي الله عنهم held an opinion and other Companions رضي الله عنهم differed with him, the opinion of the rightly-guided caliph would take precedence. 
He does not go on to say anything beyond that conclusion.
Ash-Shaukaani رحمه الله is one scholar who has taken this hadith to its furthest conclusion. He has, in essence, equated the sunnah of the rightly-guided successors with the sunnah of the Prophet صلى الله عليه وسلم. He stated,
The scholars have had lengthy discussions on this point and have tried to reinterpret the hadith in ways that are mostly farfetched. What one must conclude and follow is [that we are] to act upon what these words mean in their context in Arabic. The sunnah is the path. It is as if he said, "Stick to my path and the path of the rightly-guided successors." It is as if their path is the same as his path. They were the people who were the strictest in guarding the sunnah and following it in everything. In any case, they were very careful about differing from the sunnah in even the smallest matter, not to speak of the larger matters. If they did not have any evidence from the Book of Allah or the sunnah of the Messenger of Allah صلى الله عليه وسلم, they would act in accord with what was apparent to them of personal opinion, after searching, researching, consulting others and pondering the matter. This opinion, when there is no evidence, is also part of his [the Prophet's صلى الله عليه وسلم] sunnah . . . If you [the listener] say: If what they acted upon of personal opinion is also of his sunnah, then there is no point to him saying, "and the way of the rightly-guided successors." I respond: The benefit of this statement is that there are people who were not alive during the time of the Prophet صلى الله عليه وسلم but were alive during the time of the rightly-guided caliphs رضي الله عنهم or were alive during the time of the Prophet صلى الله عليه وسلم and of the rightly-guided caliphs رضي الله عنهم but something was done that was not done during the Prophet's time, but the caliphs did it. So directing one to the practice of the rightly-guided caliphs رضي الله عنهم removes any doubt or confusion in the soul of the person and [this hadith] makes his mind clear to follow them. The least point that one can make from this hadith is that the personal opinion that comes from the caliphs, if it is to be considered from [the Prophet's صلى الله عليه وسلم] sunnah as was stated, must take precedence over other personal opinion when no evidence is present. 
On the other hand, al-Sanaani رحمه الله takes a much more restricted approach. He stated that all what is meant by following the sunnah of the rightly-guided caliphs رضي الله عنهم is to follow them in that which they follow the sunnah of the Prophet صلى الله عليه وسلم, concerning jihad against the unbelievers, establishing the practices of the religion and so forth. 
Not everyone is of the opinion that the "rightly-guided successors" رضي الله عنهم as mentioned in this hadith are only Abu Bakr, Umar, Uthmaan and Ali رضي الله عنهم. Al-Qaari رحمه الله, for example, states that "it is said," that it is these four but later he says, "It is also said" that it refers to all of the scholars of Islam (mujtahideen ), as they are the successors to the Prophet صلى الله عليه وسلم in that they revive the truth, guide the people and raise the banner of Islam. Al-Qaari رحمه الله himself does not state which view he prefers. 
Al-Mudaabaghi رحمه الله states that the successors are first and foremost the Companions رضي الله عنهم in general. 
The problem with this view is that it makes what the Prophet صلى الله عليه وسلم specifically told them almost meaningless. It would mean that the Prophet صلى الله عليه وسلم told his Companions رضي الله عنهم, "You will see lots of differences, so follow my sunnah and your sunnah and stick to them . . ." Allah knows best, but this seems to be a strange bit of advice. One could understand him telling them that they should stick to the leaders of the Companions رضي الله عنهم who are rightly-guided and sure to follow the way of the Prophet صلى الله عليه وسلم in their own personal rulings (ijtihaad).
In his commentary to this hadith, as-Sindi رحمه الله makes no explicit mention of Abu Bakr, Umar, Uthmaan and Ali رضي الله عنهم. He stated that the meaning of the rightly guided successors are the Imams who are followed and the respected scholars of deep knowledge. 
Hence, he is not restricting it to the above mentioned four caliphs رضي الله عنهم. According to this understanding, during times of confusion and trials, one should follow the way of the Prophet صلى الله عليه وسلم as well as the way of the well-known accepted leaders and scholars of Islam.
In his commentary to this hadith, Shaykh ibn Uthaimeen رحمه الله wrote, "[The word] khulafaa' (خلفاء) is the plural of khaleefah (خليفة): they are the people who succeed the Prophet صلى الله عليه وسلم among his Nation in knowledge, actions, calling to Islam, jihad and rule. At the head of them are the four rightly-guided caliphs, Abu Bakr, Umar, Uthmaan and Ali, may Allah be pleased with them. May we be joined with them in the gardens of pleasure. These four caliphs and the successors of the Nation who come after them, those who succeed the Prophet صلى الله عليه وسلم in this Nation, they are the ones whose paths we are ordered to follow. But one must realize that the sunnah of these successors comes after the sunnah of the Messenger صلى الله عليه وسلم. If there is any conflict between the sunnah of any of these successors with the sunnah of the Prophet صلى الله عليه وسلم, the rule is with the sunnah of Muhammad صلى الله عليه وسلم and with no one else. This is because their sunnah comes after or follows the sunnah of the Prophet (peace be upon him)." 
As evidence for his last statement above, ibn Uthaimeen رحمه الله quotes ibn Abbaas رضي الله عنهما who said, "Soon I would expect rocks to fall upon you from the sky when I say, 'The Messenger of Allah صلى الله عليه وسلم said something, ' and you answer, 'Abu Bakr and Umar رضي الله عنهما said. "' That is with respect to Abu Bakr and Umar رضي الله عنهما. What then, says ibn Uthaimeen رحمه الله, must be the case with those who are less in stature than Abu Bakr and Umar? 
Elsewhere, while discussing the same point, Shaykh ibn Uthaimeen رحمه الله stated that one must follow what the Prophet صلى الله عليه وسلم said and excuse any Companion who may have said anything that goes against what the Prophet صلى الله عليه وسلم said. Such a statement must be from his personal reasoning and judgment, for which he may be excused. 
Muhammad Al-Ashqar رحمه الله also does not agree that the rightly-guided successors are the four well-known caliphs رضي الله عنهم. Al-Alaai رحمه الله had stated that there is a consensus that the rightly-guided caliphs are the four and only those four caliphs رضي الله عنهم. Al-Ashqar رحمه الله wrote the following footnote to that statement of al-Alaai's رحمه الله,
"I do not know where that consensus came from. Just because it became customary to use that term for those four does not mean that the Muslim Nation did not have any rightly-guided successor after them. The hadith describes the attribute and does not identify who the people are. Every successor (caliph) who is pious and rightly-guided, following the truth, desiring the truth and not following his desires in his rule and what he orders and prohibits is a rightly-guided caliph. It would be a consensus only if the people of consensus would say that there is no rightly-guided caliph after those four. God forbid that they should say that. Furthermore, the hadith that the author [al-Alaai رحمه الله] quotes is contradicted by many other hadith; such as the hadith, "The khilaafah will stay among the Quraish until the Hour is established." . . . 
But al-Ashqar's final argument does not seem to be very strong. All of the other hadith he quotes simply mention successors but do not mention them as being rightly-guided, right-principled. Therefore, one could argue that the Prophet صلى الله عليه وسلم was specifically referring to a special group of successors, distinguishing them from the others, and not saying that these would be the only successors. Later successors might even by rightly-guided but not to the extent of the first four caliphs. Hence, they would be deserving of such an honorific title.
Conclusion Concerning the Meaning of This Passage
All scholars seem to agree that the expression, "rightly-guided successors" applies first and foremost to Abu Bakr, Umar, Uthmaan and Ali رضي الله عنهم. The question is whether this expression is pointing to them only or is it more general and, therefore, refers to all rightly-guided successors who follow the way of the Prophet صلى الله عليه وسلم.
If the expression is taken in a more general sense, the hadith is of little value from a legal theory point of view. In other words, it points to the importance of following those who follow the way of the Prophet صلى الله عليه وسلم, yet it is agreed upon that the ijtihaad of later scholars is simply their ijtihaad and other scholars are not bound to follow what they concluded. If the expression is taken to mean the four rightly-guided caliphs رضي الله عنهم only, the question is to what extent must one follow the views of those four rightly guided caliphs رضي الله عنهم. When they make ijtihaad, is it binding on all others? It seems that such was not the understanding of the Companions رضي الله عنهم themselves. Many of them differed with the four rightly-guided caliphs on different issues of ijtihaad. Indeed, Umar رضي الله عنه even differed with Abu Bakr رضي الله عنه on some matters of ijtihaad.
From the above, it seems that this hadith is not a hadith pointing to the obligation of following the ijtihaad of either the four rightly-guided caliphs or of particular later scholars who follow the way of the Prophet صلى الله عليه وسلم.
Put into the entire context of the hadith, this statement seems to be pointing to a broader concept. Innovations and differences have appeared and continue to appear among the Muslim nation. In this hadith, the Prophet صلى الله عليه وسلم instructed Muslims how to react to such innovations and differences. One does not follow such innovations and new ideas. Instead, one sticks to the way of religion of the Prophet Muhammad صلى الله عليه وسلم and those who adhered to his path, who are first and foremost Abu Bakr, Umar, Uthmaan and Ali رضي الله عنهم, and secondly the remainder of the Companions رضي الله عنهم and great scholars throughout Islam رحمة الله عليهم. Their approach to the religion is the one and only correct approach to Islam- this is different from saying that they were correct in their individual ijtihaad. Their refusal to stray from the way of the Prophet صلى الله عليه وسلم, their refusal to introduce new beliefs or concepts into Islam, their strict adherence to the sunnah in all matters, large or small, these are the type of matters concerning which they are setting the supreme example. One should not stray from their general approach in the least. Any straying from their approach to Islam is a misguidance and heresy.
Now the Muslim has many examples or guides that he can look to in the face of differences and new ideas that cropped into Islam. He can see how the Prophet صلى الله عليه وسلم dealt with such ideas or comparable situations. If they did not exist during the Prophet's صلى الله عليه وسلم time, he can look at how the four rightly-guided caliphs رضي الله عنهم dealt with such or similar issues. If they did not encounter the problem, he can see how the other Companions رضي الله عنهم dealt with such an issue. If even there the situation was not dealt with, he can look to see how the well-known and accepted scholars who adhered to the way of the Prophet صلى الله عليه وسلم and his pious successors dealt with such an issue. The Muslim should cling dearly to their ways. When he does this, he will be safe from innovations and misguidance. Allah knows best.
"Bite onto that with your molar teeth..."
The Prophet صلى الله عليه وسلم referred to his sunnah and the sunnah of the rightly-guided successors رضي الله عنهم as being one entity. [In other words, he said 'alayhaa (عليها) instead of 'alayhimaa (عليهما). The latter ('alayhimaa) would be translated as, "stick to those two," instead of, "stick to that."]
This implies the closeness between the two and the fact that they were following the same path as his path. This is further evidence that the path of lslam is one and not many. 
There is only the correct path of the Prophet Muhammad صلى الله عليه وسلم. His path is one path and it is the same path as the path of the rightly-guided successors رضي الله عنهم after him. Anyone who claims any other way has fallen into innovations and misguidance.
The exhortation to bite onto their way with one's molar teeth is a way of expressing how closely one should adhere to their path. One must cling to their way in a manner similar to how one bites onto something with one's molar teeth. If anyone tries to pull away what the person is biting on, it would be difficult. Similarly, it would be very difficult to pull the believer away from the path of the Prophet صلى الله عليه وسلم and his followers who tread his path. This portion of the hadith, as al-Haitami رحمه الله points out, may also be implying the type of patience that it takes to strictly adhere to the path of the Prophet صلى الله عليه وسلم. One must have great patience to stick to that path and the only way that can be done is to stick to it in a manner similar to the way one bites onto something with his molar teeth.  
 Abu Dawood and at-Tirmidhi, according to ibn Muhammad, al-Albaani, al-Bazzaar, al-Tirmidhi, al-Haakim, ibn Abdul Barr, Abu Nuaim and numerous others, this is an authentic hadith
 Recorded by at-Tirmidhi. According to Shaykh al-Albaani رحمه الله, it is sahih. See al-Albaani, Saheeh al-Jaami, vol. 1 , p. 630.
 Al-Nawawi, Sharh Matn al-Arbaeen, p. 1 1 5; ibn al-Arabi, vol. 1 0, p. 146; ibn Daqeeq al-Eid, Sharh, p. 75; al-Teebi, vol. 2, p. 634; Khaleel al-Alaai, Ijmaal al-/saabahji Aqwaal al-Sahaabah (Kuwait: Jameeah lhyaa al-Turaath al-Islaami, 1 987), p. 49; ibn Rajah, Jaami, vol. 2, p. 122; alTahaawi and ibn Abu al-Izz in Sharh al-Aqeedah al-Tahaawiya, vol. 2, p. 726; alMubaarakfoori, vol. 7, p. 441 ; Suhaaranfoori, vol. 1 8, p. 147; al-Rasheed, p. 342; Abdul Azeez al-Salmaan, al-Kawaashif al-Jaliyyah an Maani al-Waasitiyah (198 1), p. 748; al-Bugha and Mistu, p. 202; Sultaan p. 253. lbn Rajab also points out that some people include Umar ibn Abdul Azeez رحمه الله as the fifth of the rightly-guided caliphs.
 Al-Haitami, Fath, p. 220.
 Recorded by at-Tirmidhi, ibn Maajah and Ahmad. According to Shaykh al-Albaani رحمه الله, it is sahih. See al-Albaani, Saheeh al-Jaami, vol. 1 , p. 254.
 Quoted in ibn Rajab, Jaami, vol. 2, p. 1 23.
 Al-Alaai, Ijmaal, p. 47.
 An-Namlah, vol. 4, p. 99.
 For examples, see al-Alaai, Ijmaal, p. 48.
 Cf., al-Alaai, Ijmaal, p. 49.
 Ibn al-Arabi, vol. 10, p. 147; ibn Daqeeq al-Eid, Sharh, p. 75.
 Suhaaranfoori, vol. 18, p. 1 47.
 Quoted in al-Mubaarakfoori, vol. 7, pp. 440-44 1 .
 Quoted in al-Mubaarakfoori, vol. 3 , pp. 50-5 1 .
 Al-Qaari, vol. I , pp. 242-243.
 Al-Mudaabaghi, p. 220.
 As-Sindi, Sharh al-Arbaeen, p. 94.
 lbn Uthaimeen, Sharh Riyaadh, vol. 3, pp. 338-339.
 lbn Uthaimeen, Sharh Riyaadh, vol. 3, p. 340.
 ibn Uthaimeen, Sharh al-Aqeedah al-Waasitiyah, vol. 2, p. 3 14.
 Muhammad al-Ashqar, footnotes to al-Alaai, ljmaal, pp. 49-50.
 Cf., Taataay, pp. 234-235.
 Cf., al-Haitami, Fath, p. 221 .
 Commentary on the 40 Hadeeth of Imam an-Nawawi رحمه الله, vol. 2, pp. 874-882
The Sahabah (Companions - may Allaah be pleased with them all) - http://www.muftisays.com/forums/36-nabi-s--sahaabah-stories/5863-the-sahaba-companions-radiallaahu-anhum.html