Dattatreya is considered as incarnation of the Divine Trinity, Brahma-Vishnu-Maheshwara. The word Datta means "Given," given in the form of a son to the sage couple Atri and Anasuya. He is the son of Atri, hence "Atreya."
Once Brahma-Vishnu-Maheshwara went to Anasuya (wife of great sage Atri) requesting alms. When she agreed to do so, they asked her to serve the food without wearing clothes. Since appearing naked in front of other men will reduce her Pativritya (devotion to her husband), by the power she had she made them children and then breastfed them. These children, then became Soma (Brahma), Vishnu (Dattatreya), Shiva (Durvasas) and then Dattatreya stayed with his parents and considered as Trigunatmaka (containing the character of Trinity, Brahma-Vishnu-Maheshwara).
Brahmanandam Brahma Mukundam bhagavantham
Brahmajnaanam Sathyamanatham Bhaavaroopam
Poornam Chidhghana Panchamakandam Shivaroopam
Dattatreyam Shri Gururoopam Shivaroopam
Om Shaanthaakaaram Sheshashayanam Suravandhyam
Kaanthaanaatham Komalagaathram Kamalaaksham
Chintaarathnam chidhghanapoornam dwijaraajam
Dattatreyam Shri Gurumoorthim Pranathosmi
Om Aaam Hreem Krom Ehi Dattatreya Swaaha