Avatar, Avatara (Sanskrit) [from ava down + the verbal root tri to cross over, pass] That which passes down or descends; the passing down of a celestial energy or an individualized complex of celestial energies -- a celestial being -- in order to overshadow and illuminate a human being. "Hence an Avatara is one who has a combination of three elements in his being: an inspiring divinity; a highly evolved intermediate nature or soul, which is the channel of that inspiring divinity; and a pure, clean, physical body".
Sankaracharya, Krishna, Lao-tzu, and Jesus were avataras in differing degrees, of somewhat differing structure. There was a divine ray which came down at the cyclic time of each of these incarnations, and the connecting link or the flame of mind was provided in each case by a member of the Hierarchy of Compassion. Krishna says, "I incarnate in period after period in order to destroy wickedness and reestablish righteousness" (BG ch 4, sl 8). An avatara takes place when a direct ray from the Logos enters into, fully inspires, and illuminates, a human being, through the intermediary of a Bodhisattva (one who has attained Enlightenment but postpones entry into Nirvana in order to help others to also achieve Enlightenment), who has incarnated in that human being, thereby supplying the fit, ready, and fully conscious intermediate vehicle or carrier" (Fund 276).
Vishnu as the supporter of life is the source of one line of avataras so often spoken of in Hindu legends. These ten avataras of Vishnu are: 1) Matsya the fish; 2) Kurma the tortoise; 3) Varaha the boar; 4) Narasimha the man-lion (last of animal stage); 5) Vamana the dwarf (first step toward the human form); 6) Parasu-Rama, Rama with the axe (a hero); 7) Rama-chandra, the hero of the Ramayana; 8) Krishna, son of Devaki; 9) Gautama Buddha; and 10) Kalki, the avatara who is to appear at the end of the kali yuga mounted on a white horse, inaugurating a new reign of righteousness on earth. A horse has from immemorial time been a symbol of the spiritual as well as vital energies of the inner solar orb. Hence, when the next avatara is said to come riding a white horse, the meaning is that he comes infilled with the solar light or splendor -- an avatara or manifestation of a spiritual and intellectual solar energy which will carry all before it on earth.
Brahmanical esotericism never taught that divinity descended into the animals as given in the legends. These names of different animals and men, like all zoological mythology, were chosen because of certain characteristic attributes. They actually represent ten degrees of advancing knowledge and growth in understanding -- ten degrees in the esoteric cycle -- as well as different evolutionary stages through which monads break through the lower spheres in order to express themselves on higher rungs of the evolutionary ladder of life. These names also represent the technical names given to neophytes in esoteric schools. The lowest chela was called a fish, the chela who had taken the second degree successfully was called a tortoise, and so forth, till the highest of all was called an incarnation of the sun -- a white horse in Hindu legend.