The death of Jesus was a sacrifice to provide the same kind of benefit as the Old Testament animal sacrifices. When there is sin, something simply must be done about it. The only proper responses are: (1) admitting it, (2) repenting from it, (3) making restitution for it to those harmed by it, (4) pleading to God for mercy and forgiveness. Old Testament animal sacrifice has these elements.
We don't take Jesus to the temple to sacrifice him; he offered himself as our sacrifice. We, instead, offer up his one time sacrifice. This is done is a very tangible way during mass but sadly, the Eucharist is rejected by many Protestants.
The sacrificial aspect of redemption is for our benefit, to provide a way for us to interact with Jesus' work. Jesus provides for redemption through the incarnation and deification of human nature and the universe;we participate in this through the sacrificial aspects of Jesus' work. In effect, we present Jesus before God as a sacrifice on our behalf and God pardons our sins. (But we don't sacrifice Jesus over and over again.)
We are in Satan's kingdom. In Old Testament times Christ had not yet died (nor was born). Satan's goal is to kill Christ, so in creating this worldGod promised Satan that forgiveness for sin would require a death; that way, when Christ was born, Satan could kill him pretending he was doing so to allow other people's sins to be forgiven. (Satan didn't realize Christ would rise from the dead and conquer sin, death, and Satan).
God taught Adam and Eve how to sacrifice animals; they taught Abel, etc. (Adam was not the first human, rather, he was the first human of redemption history. Religion and animal sacrifices began at that time, instituted by God.) The death of the animal really does cause redemption. (Those performing human sacrifice sensed there was real spiritual power in death — but not of a good kind).
Before the fall of humanity there was no need for redemption — all were redeemed. Satan was waiting for the chance to begin destroying human souls. God had promised him this opportunity; if Adam and Eve chose Satan over God, Satan could set up his kingdom of darkness. Satan only rules over people who are alive; after death they were placed in Abraham's Bosom for safety (but the wicked suffered there as we see in the account of Lazarus and the rich man.)