Greece/Rome religion
How it changed
Greece previous religion
People practiced the religion of their community, their political state and did so to ensure the gods they honored protected them and sustained their communities. Christianity changed all this by bringing in a far more exclusivist idea of religion from its parent religion, Judaism. To the Christians, the other gods weren't just irrelevant, they were non-existent. other cults weren't just not useful, they were evil. This was one of the things which brought Christianity into conflict with the Roman state, which saw them as an insult to the protective gods of the Empire and therefore a threat to the state.
The Greeks had always been polytheistic. They believed that there were gods that influenced their lives. They thought the gods would respond to worship and acts of piety.
The Romans looked between their gods and the greek gods to find a midpoint. They would claim that any success they had was due to good relations with their gods.
Roman emperor Constantine
When the Roman emperor constantine converted to Christianity, the balance of power changed. Christianity was now made legal and Constantine sponsored it with church building programs and other endorsements. Over the next century Christians went from representing about 10% of the empires population to becoming an overwhelming majority. The emperor Theodosious eventually made Christianity the official state religion in 380AD. Paganism was never banned, though its public practice and it's practice as official state events was.
Sacrifices
These gods and sacred functions and objects seemed charged with power because they were mysterious and alarming. In order to secure their food supply, physical protection, and growth in numbers, the early Romans believed that such forces had to be propitiated and made allies. Sacrifice was necessary. The product sacrificed would revitalize the divinity, which was seen as a power of action and therefore likely to rundown unless revitalized. By this nourishment that he or it would be able to fulfill request. The phrase mate esto was said during sacrifices (be you increased)