What is the idea behind animal sacrifice in religion?

There have been, and probably still are, religions that practice animal (and sometimes human) sacrifice. The temple of Solomon was primarily used as a place where people brought their animals for ritual sacrifice by the priests. What is the idea behind such acts? Did people think that the gods would somehow make use of the animal? Was the sacrifice of a prized animal a way of demonstrating one’s faith? Or was it simply something demanded by the gods?