The most famous avatars in the Hindu tradition are the "Ten Avatars" of the god Vishnu: The Fish, The Tortoise, The Boar, The Man-Lion, The Dwarf, Parashurama, Rama, Krishna, Buddha, and Kalki (although the list differs in some details from one Hindu tradition to another). You can read more about the incarnations in this Wikipedia article: Dashavatara.
In English, the word "avatar" has become especially associated with the way human beings are represented in the environments created by digital computers. The Oxford English Dictionary cites an examples of this usage from 1986, although the most famous early example is the use by Neal Stephenson in his marvelous science fiction novel Snow Crash, published in 1992, which happens to be one of my all-time favorite science fiction novels!
Meanwhile, this lovely painting shows the "Dasavatara," the Ten Incarnations of Vishnu: