Allaah سبحانه و تعالى says,
"Have they not pondered over (yaddabbaroo) the Word (of Allaah سبحانه و تعالى, i.e. what is sent down to the Prophet صلى الله عليه وسلم), or has there come to them what had not come to their fathers of old?" (Sooratul Mu'minoon, 23:68)
"(This is) a Book (the Qur'aan) which We have sent down to you, full of blessings that they may ponder over (liyaddabbaroo) its Verses, and that men of understanding may remember." (Soorah Saad, 38:29)
"Do they not then consider (yatadabbaroon) the Qur'aan carefully? Had it been from other than Allaah, they would surely have found therein much contradictions." (Sooratun-Nisaa', 4:82)
Shaykh Muhammad 'Umar Baazmool said,
"At-Tadabbur (التَّدَبُّرُ) linguistically derives from the Arabic word ad-dubur [الدُّبُر] which is the end of something. Dubr ad-Daabah, i.e. the end of the riding beast. Tadbeer and tadabbur of an affair is the consideration of the consequences of the affair, i.e. to consider what the end result will lead to. At-tadabbur is thinking on it, i.e. the acquirement of two pieces of information to acquire a third. Therfore at-tadabbur is thinking and understanding.
At-tadabbur and al-i'tibaar (consideration): a lesson or example; consideration of the past. Al-i'tibaar: contemplation and discernment.
Therefore al-i'tibaar is the condition and psychological framework with which the knowledge of something observed leads to the knowledge of something unobserved.
In conventional language: at-tadabbur is a term meaning the consideration of the consequences of things, and it is similar in meaning to the term at-tafakkur (التَّفَكُّرُ) (i.e. thinking), although thinking is the behaviour of the heart when considering a proof, and tadabbur is the behaviour of the heart with the consideration of the final consequences. 
And in the Islaamic legislation: at-tadabbur is the consideration, understanding, and thinking about the consequences to which the affairs mentioned in the Noble Qur'aan lead, and the benefits from that in regards to the servants eemaan, and the appearance of its effects on the limbs."  
 Lisaan al-'Arab; al-Qaamoos al-Waseet; Taaj al-'Aroos.
 Imaam al-Jurjaanee رحمه الله: At-Ta'reefaat.
 Contemplation Of The Qur'an & Its Effect Regarding Purification Of The Soul, p. 6.