An organization led by the most powerful human and High Elf mages in the world. They founded the city of Dalaran as a place to study and teach the ways of magic. One of their task was to safeguard and wield the Eye of Dalaran
Sometime later, the term "Kirin Tor" refered to the Magus Senate of Dalaran, and later is sometimes mistakenly attributed to the Six of that body which consisted of six members only. (In "Day of the Dragon" there are six members of the Six of the Kirin Tor. "The Last Guardian" mentions seven Kirin Tor and lists five by name. Antonidas, Jaina and Kel'Thuzad are the only ones mentioned in the games.)
The Kirin Tor government is divided into two sections, each with two sections within itself. The two Councils are the Six and the Twelve - the Six being based on seniority, the Twelve elected (usually votes go based on magical power). The other group are the Archmages, who actually carry out the instructions of the Six and the Twelve. They are divided into the Mages' Union and the Sorcerers' League. It is also often known that the Six and the Twelve do not always agree, and as they hold equal power, it is usually a case of the right hand not knowing what the left was doing. It did not ever come to violence, though.
However, some mages of the Kirin Tor delved too deeply into necromancy, demonology, and other warlock magics. One of the most powerful, Kel'Thuzad, was expelled from the Kirin Tor and decided open a rival school of magic, mostly necromancy: the Scholomance. There, he and his students created the Plague of Undeath, which ravaged Azeroth and led to the rise of the undead Scourge. Kel'Thuzad himself became a powerful Lich, and chief lieutenant to the Lich King.
What is left of the Kirin Tor strive to rebuild their once magnificent capital of Dalaran.