Atri Maharshi and his wife Anusuya by the fruits of their austerities begot the divine Trinity i.e. Brahma, Vishnu and Mahesh as their off-spring. The Sage named the young Vishnu as "Datta", the charming Brahma as "Chandra" and the infant Siva as "Durvasa". The three being son's of Atri Maharshi, were called as "Atreyas" and Datta came to be called "Dattatreya". After some time, with the permission of their mother, Anusuya, Chandra (Brahma) and Durvasa (Siva) merged their divinity in Datta and retired for doing penance. The Supreme Spirit, henceforth known as "Dattatreya", is indeed unbound by phenomenal existence. Yet, in deference to a curse laid on him once by the sage Durvasa, he ever abides on earth, assuming different human forms. This he does out of compassion for the creatures on earth and for the gods. There were avatars of the Lord earlier too, but all of them, after completing their mission, left off those forms and returned their one essence. In order to bless his devotees, the Lord had incarnated as Lord Dattatreya, yet he did not, like the other avatars, leave the earthly plane of existence after accomplishing his divine mission.
As this mission has to be carried out as long as creation exists, he does not lay down his body and leave for his heavenly realm but goes on wandering from place to place. Thus Dattatreya is the eternal avatar of God's Spirit of self dedication to the salvation of all creatures. He manifests himself perennially as the perfect saints of all religions of the world. Lord Dattatreya is also refereed to as the Adi-Guru (The primeval Teacher).
( Also refer "Sree Guru Charitra" (English) by Pujya Sri Acharya Ekkirala Bharadwaja)