Paul was a Jew as well as a Roman citizen.
As a Jew, he would have been familiar with the animal sacrifices that his people made in atonement for sin. In his epistles he often expands on the idea that Jesus came in lieu of all animal sacrifices for all sins for all times.
As a Roman citizen, he lived in a time and place where relatively few people enjoyed the benefits of citizenship. Most people were not citizens and had very few rights. In ancient Rome, a person could "buy" citizenship by performing various actions, including animal sacrifice to the Roman gods. In his epistles, Paul refered to how Jesus' crucifixion made us citizens of God's kingdom analogous to the way a weathy person could become a Roman citizen by making offerings to the Roman temples.