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)