The words translated here as, "Fear Allaah," are اتق الله. That is, one should have "taqwa of Allaah." Taqwa is one of the most important concepts found in the Qur'an and Sunnah. Indeed, al-Mubaarakfoori رحمه الله calls it the foundation of the religion. 
In numerous Ahaadeeth, the Prophet صلى الله عليه وسلم advised Muslims to have taqwa. Whenever he sent an army out, he would advise them to have taqwa of Allaah سبحانه و تعالى. Indeed, this has been the command of Allaah سبحانه و تعالى for all of the Messengers عليهم الصلاة والسلام.
Allaah سبحانه و تعالى says,
"And to Allaah belongs all that is in the heavens and all that is in the earth. And verily, We have instructed those who were given the Scripture before you, and to you (O Muslims) that you (all) fear Allaah, and keep your duty to Him, But if you disbelieve, then unto Allah belongs all that is in the heavens and all that is in the earth, and Allah is Ever Rich (Free of all wants), Worthy of all praise." (Soorah an-Nisaa', 4:131)
Commenting on this verse, Imaam al-Ghazzaali رحمه الله wrote,
"Does not Allaah سبحانه و تعالى have more knowledge than anyone concerning what is best for the human? Is He not their most sincere adviser and more merciful and compassionate than anyone? If there were any characteristic that is better for a human, more comprehensive in its goodness, greater in its reward, more important for worship, weightier in measure, more important in its substance and more rescuing in the long-run than this characteristic of taqwa, then Allaah سبحانه و تعالى would have ordered His servants to have that other characteristic. Allaah سبحانه و تعالى has advised his most dear servants to have this characteristic out of His Perfect Wisdom and Encompassing Mercy.
When he advised this one characteristic, and combined together His previous and later servants upon that characteristic and mentioned that characteristic only, you then know that it is the final goal beyond which there is none other and for which there is no other purpose. Allaah سبحانه و تعالى has combined together every advise, direction, guidance, instruction, teaching and rectification in that one advice, as is becoming His Wisdom and Mercy. And you also know by that fact that this one characteristic of taqwa combines together all of the good of this life and the Hereafter, that is sufficient for all of the important matters that leads one to the highest ranks [in Paradise]. This foundation cannot be increased upon. It is sufficient for the one who sees the light, is guided and acts upon that light." 
Furthermore, in numerous places in the Qur'an, Allaah سبحانه و تعالى has quoted different Prophets and Messengers عليهم الصلاة والسلام as advising their people and telling them that they must have taqwa of Allaah. These are the most sincere of all who give advice. Such was the example of Saalih, Lot, Moses and others عليهم الصلاة والسلام.
For example, Allaah سبحانه و تعالى says about Noah عليه السلام,
"The people of Nuh (Noah) belied the Messengers. When their brother Nuh (Noah) said to them, 'Will you not fear Allaah?'" (Soorah ash-Shu'araa, 26:105-106)
A lexical understanding of the word taqwa will help in having a complete picture of this very important concept. In the supplement to Lane's Lexicon, it defines اتّقى in the following manner,
"He preserved, or guarded, himself exceedingly, or extraordinarily; he put a thing between him and another to preserve him, or guard him. In the conventional language of the law, he preserved, or guarded, himself exceedingly, or extraordinarily, from sin, of commission or of omission.... It may often be rendered, he was pious, or careful of his religious duties." 
The essence, therefore, of Taqwa is to put some kind of barrier or guard between oneself and what one fears, in order to protect oneself from what is feared. A form of this word was used, in its linguistic sense, in a Hadeeth in Saheeh Muslim. Al-Baraa' رضي الله عنه was describing the Battle of Hunain in which many Muslims fled but the Prophet صلى الله عليه وسلم did not flee. At one point in the Hadeeth, he stated, "By Allaah, if the fighting became hot, we would seek a barrier or protection (nattaqee) in the Prophet صلى الله عليه وسلم. And the brave one among us was the one who was next to him, that is, next to the Prophet صلى الله عليه وسلم."
That is, they would put the Prophet صلى الله عليه وسلم between themselves and the enemy in order to protect themselves from the enemy, due to the Prophet's courage and bravery صلى الله عليه وسلم.
As was noted above, the word taqwa is sometimes followed by the name of Allaah سبحانه و تعالى (have taqwa of Allaah). This is the case with this particular Hadeeth and with numerous verses of the Qur'aan (such as al-Maa'idah 96 and al-Hashr 18). Again, in this sense, it means one should fear or protect himself from Allaah's anger and punishment. This can only be done by obeying Him and not disobeying Him. This is the minimum aspect of taqwa. 
Furthermore, if someone puts some kind of distance between himself and disobeying Allaah سبحانه و تعالى, then he has fulfilled what this concept of taqwa really implies. Abud-Dardaa' رضي الله عنه and al-Hasan رحمه الله have both stated that the people of taqwa even leave permissible deeds out of fear that there might be something harmful in them. These doubtful or permissible acts are that barrier that they have put between themselves and the acts of disobedience.
Sometimes the word is followed by the place of Allaah's punishment, such as Hell, or to the time of Allaah's punishment, the Day of Resurrection. The meaning is once again the same: One must protect himself from the harm related to those times or places.
Here are two examples from the Qur'an, 
"And fear the Fire, which has been prepared for the disbelievers." (Soorah Aali 'Imraan, 3:131)
"And fear a Day (of Judgement) when a person shall not avail another, nor will intercession be accepted from him nor will compensation be taken from him nor will they be helped." (Soorah al-Baqarah, 2:48)
 Al-Mubaarakfoori رحمه الله, Tuhfah, vol. 6, p. 122. One may note an emphasis in the Sharee'ah on the concept of "protection" and "guarding," that is, "guarding against shirk, evil, sins and so forth." Ja'far Shaikh Idris explained this concept by stating that the true nature of humans (the fitra) is one of obedience to Allaah سبحانه و تعالى. This nature simply needs to be guarded and protected from straying and it will be led to Paradise. That is the reason for emphasis on protection, guarding and taqwa. (Ja'far Shaikh Idris, Personal Interview, Farfax, VA, @ Feb. 1996.)
 Quoted in Ahmad Fareed, at-Taqwa: al-Ghaayah al-Manshuwudah wad-Durrah al-Mafqoodah (Riyadh: Dar as-Samee', 1993), p. 18
 Lane, vol. 2, p. 3059
 Al-Baghawi رحمه الله wrote, "It is as if the person of taqwa places the implementation of Allaah's command and avoidance of what He has forbidden as a kind of barrier between himself and the punishment." al-Hussain al-Baghawi, Tafseer al-Baghawi: Ma'alim at-Tanzeel (Riyadh: Daar Taiba, 1409 A.H.) vol. 1, p. 60
 Shaykh Jamaaluddeen Zarabozo, Commentary on the Forty Hadeeth of Imam An-Nawawi رحمه الله, vol. 1, pp. 575-578