Datta Homam or Sri Dattatreya Homam is the fire-worship of Lord Dattatreya. Lord Dattatreya is considered an incarnation on earth and is worshipped by millions within the Hindu community. The Datta Homam is performed like any other homam by making offerings to the fire and seeking the blessings of the Lord, also referred to as just Datta.
Datta Homam is performed to propitiate Lord Dattatreya. If you visit Dattatreya temples you can see His idol with three heads, six hands, and four dogs, standing in front of the divine cow and wish-fulfilling tree (KalapakaVriksh). Some believe He is the combined incarnation of Lords Brahma, Vishnu and Shiva. He is considered the ultimate Guru and there is a belief that Shirdi Saibaba was an incarnation of Lord Dattatreya. Datta Jayanthi is celebrated in a big way across India.
Datta Homam is performed to seek the blessings of Lord Dattatreya for prosperity, wealth and a better life. If your astrologer, after reading your horoscopes advises that performing Datta Homam can solve some of your problems, you can have the homam arranged.
By performing Datta Homam, you can hope to gain in wealth and prosperity. There are couples who seek the birth of a child by performing Datta Homam. The general purpose and benefits are related to material aspects of life. Lord Dattatreya is believed to offer these to His devotees.
You should leave the conduct of Datta Homam to professionally trained pandits from Swarnatara Spirituals.