In Sanskrit avatar literally means "descent," or, in a broader sense the term means the reincarnation of the same soul in a different body. In Hinduism avatar is a human incarnation of the Divine who functions as a mediator humans and God. The incarnations Vishnu, the sky god and protector of the universe, are examples of avatars.
This "descent" meaning of the word is expressed in the sacred writings of the Ramayana and Mahabharata (the latter includes the Bhagavad-Gita); however this meaning is not present in the Vedas nor the Upanishads.
The avatars appearing in the previous mentioned sacred writings are Rama and Krishna the last incarnations of Vishnu and the of the most beloved and worshiped gods in the Hindu pantheon. Krishna is considered the perfect example of the Divine.
Vishnu is believed to have had anywhere from ten to thirty-nine incarnations, although the potential number of avatars are numerous. Each avatar appears when the world is in crisis. Vishnu's final avatar is believed to be Kali, appearing at the end of Kali Yuga, a present era, and will destroy the wicked to usher in Maha Yuga, a new era.
Hindus believe Gautama Buddha to be an avatar.
There are devotional movements, called bhakti, in Hinduism which center themselves around avatar figures. Such movements claim to derive the avatar's siddhis or psychic abilities and paranormal powers such as to levitate, bilocate, and such. A.G.H.
Guiley, Rosemary Ellen, Harper's Encyclopedia of Mystical and Paranormal Experience, New York: HarperCollins, 1991, pp. 48-49
Riland, George, The New Steinerbooks Dictionary of Paranormal, New York, Warner Books, Inc., 1980, p. 20
Walker, Barbara G, The Woman's Encyclopedia of Myths and Secrets, New York, HarperCollins, 1983, p, 80