Honorary religious title meaning the teacher whose wisdom is great as an ocean. The term dalai is a Western adaptation of ta-le, the Mongolian version of the Tibetan gyatso (Tib., rGya-mtsho), "Ocean of Wisdom".
The true Tibetan title for the Dalai Lama, as it is used in Tibet, is rGyal-ba, indicating the "supreme head" of the school, believed to be an incarnation of Avalokitesvara.
The title of Dalai Lama was first bestowed (in 1578) on Sonam Gyatso, then Grand Lama of the Gelugpa school, by the Mongol leader Altan Khan, when he and his Mongols officially adopted Buddhism. Sonam Gyatso, who was seen as an incarnation of Gendun Drub, by way of Gendun Gyatso, came to be known since then as the third Dalai Lama.
Sonam Gyatso (3rd) promised the Mongolians that his future incarnation would be among them. As promised, Yonten Gyatso (4th) was a direct descendant of Altan Khan, and the only Dalai Lama ever to be born outside of Tibet. The title and office has since been carried through time by an unbroken series of reincarnations. However, the present (14th) Dalai Lama, Nobel-prize winner Tenzin Gyatso, has announced that he possibly represents "the end of the line", since he has decided not to reincarnate in the future.
A beautiful Secret Autobiography of the The Great Fifth, Ngawang Lobzang Gyatso, has been published in 1991.