The theory of Brahman as redeemer is clearly brought out by that Avatar a or Divine incarnation as revealed in the two Itihasas, the Ramayana and the Mahabharata, It is fully revealed by the author of the Bhagawad Gita who is the highest incarnation of God. As the Lord himself says in the Gtta, He incarnates into history when virtue or dharma declines and is threatened with destruction by adharma or vice. He comes down with a unique form of his own to punish the evil-doer and reward the virtuous man and restore the moral order of the world. 

The real motive of the incarnation is moral and religious as it consists in redeeming even the evil-doer from his ways of wickedness or sin and blessing the devotee or bhakta by revealing His form made of love or kripa. Even punishment or dandana is dayakarya [a work of sympathy] as its real object is to reform the offender and not repress him. Avatara is not descent from a higher place to a lower place with a physical body. It is spiritual descent into human and even subhuman planes and is due to divine love and accessibility or sahabhya.
The avataras are said to possess certain characteristics that can be recognized easily. As a child, a rudraksha mala (or string of rosary beads) will turn clockwise when held above the baby. Similarly, vibhuti will mark the palms. Such are the symbols of the avatara, and such a child is usually the subject of poojas, chanta and mantras. 

The Itihasas refer to ten chief avataras of Vishnu of which the most important are Rama and Krishna. The earlier avatar as like those of the fish, the tortoise, the boar and the man-lion and the dwarf or Matsya, Kurma, Varaha and Nara-simha and Vamana - were made on critical occasions in cosmic history to restore the cosmic moral and spiritual order and establish the kingdom of righteousness. 

Rama was born to punish the evil-doers like Ravana and establish righteous rule or Ramarajya based on the eternal rules of dharma. The Gita refers to the avatara as the very embodiment of Divine Love and they guarantee salvation or mukti to all Jivas regardless of their birth and status, including even the subhuman species. The Avatara is, therefore, extolled and adored as sarva-loka-raksaka or universal redeemer. Note that it is only Vishnu who is born as an avatara, and not Shiva. 

Usually, once his mission is accomplished, the avatara may continue his life as per the normal human pattern,and at the end of it, may take samadhi, and merge with the cosmic consciousness.