Avatar
The term "Avatar" comes from the Indian language of Sanskrit. The word Avatāra, (Sanskrit: अवतार), which means "descent"; its roots are ava, "down," and tri, "to pass." In the Hindu scriptures, avatara signifies the descent of Divinity into flesh. One who attains union with Spirit and then returns to earth to help humanity is called an avatar. The Chinese characters that appear at the top of the show's title card mean "the divine medium who has descended upon the mortal world."[30]
When Aang was young, he unknowingly revealed that he was the Avatar when he chose four toys out of thousands, each of which were the childhood toys of the previous Avatars. In Tibetan Buddhism, there is a similar test for reincarnations of a Tulku Lama. In Magic and Mystery in Tibet, Alexandra David-Neel writes that "a number of objects such as rosaries, ritualistic implements, books, tea-cups, etc., are placed together, and the child must pick out those which belonged to the late tulku, thus showing that he recognizes the things which were theirs in their previous life."[32] Each successor is expected to show signs of continuity with the previous Avatar, such as being born within a week of the death.[21]
Source: http://en.wikipedia.org/wiki/Avatar:_The_Last_Airbender