Yajna (Yagna), Yaga and Homa are the terms derived from the verbal root ‘Yaj’. Both the words Yagna and Yaga mean the same thing, worship in the form of offering oblations, a sacrifice unto the gods. It is also describerd as the ‘Tyaga’ (giving up offering) of a dravya (a specified material) unto a devata (a specific deity).
Homa is the act of pouring ajya (ghee) into the duly consecrated grhya or domestic fire. It is a later adaptation of the original yajnas and yagas and is more common in puja or the ritualistic worship of deities of the Hindu pantheon.
The general principle accepted by Hindu religious tradition is that the scriptures – the Sruti and the Smritis – are the final authority regarding the things beyond, the ultimate values of life. According to them, yajna or the system of sacrifices was given by God himself at the beginning of creation, to human beings and the gods (like Indra, Agni, Varuna and so on) as a link between them, to sustain each other. The human beings were to satiate the gods through the sacrifices and the gods, in return, would bestow on the human beings rains, food and other things needed to live a prosperous life, because they controlled the various forces of nature.
When a person performs Vedic sacrifices like Jyotistoma, say, to go to heaven, the potential effect of it in a subtle form resides in his soul and will give its fruit after death. This potential imperceptible power or sakti, is called ‘apurva’.
Human beings need light and heat to sustain themselves in life. The sun (Surya) and the fire (Agni) are the two sources for these. The sun is not under human control, but fire is. Perhaps it was this fact that might have induced our ancient ancestors to protect and maintain the fire with respect, and even worship it. It must have given the of a deity as a result of the intuitive experiences of the sages.
(Extracted from a book called “Vedic Sacrifices – An Outline”, by Swami Harshananda for Ramakrishna Math.)