Who was Sanjaya?
Sanjaya the son of Gavalgani, was the Saarathy of king DhritarAshtra. He was believed to be pious and the righteous towards his duty.
After the fall of Bhishma, Sanjaya rushes to DhritarAshtra. Being awarded with the divine vision, various chapters of the war of Mahabharata is described by him to DhritarAshtra. He is also the narrator of the whole "Bhagavad Gita".
The learned son of Gavalgana, Sanjaya, also of passions under full control, and the foremost of ministers, attained, in the Parva, to the blessed state. [Adi parva]
Where are the details about Sanjaya in Mahabharata
The details are scattered across the various chapters. You may refer sacred-texts.com to read the authentic version of Mahabharata.
Why did Sri Krishna favour Sanjaya with Divya Dirshti
VyAsa gave divya drushti to Sanjaya. It was supposed to be given to DhritarAshtra, but he didn't want to witness the terror of the great war with his own eyes.
Dhritarashtra said,--'O best of regenerate Rishi, I like not to behold the slaughter of kinsmen. I shall, however, through thy potency hear of this battle minutely."
Vaisampayana continued.--"Upon his not wishing to see the battle but wishing to hear of it, Vyasa, that lord of boons, gave a boon to Sanjaya. (And addressing Dhritarashtra he said),--'This Sanjaya, O king, will describe the battle to thee. Nothing in the whole battle will be beyond this one's eyes.' Endued, O king with celestial vision, Sanjaya will narrate the battle to thee. He will have knowledge of everything. Manifest or concealed, (happening) by day or by night, even that which is thought of in the mind, Sanjaya shall know everything. Weapons will not cut him and exertion will not fatigue him. This son of Gavalgani will come out of the battle with life. [Bhishma Parva]