Burnt offering
Once again, I'm no expert on these matters. Just putting out there what I've seen on this subject. The subject is seen in the New Testament, if memory serves. It is called a burnt offering. In Hebrew, it is called Korban.
The word doesn't translate easily into English, so I've read. It is translated to mean "sacrifice". The Jews of that time would do this in the Temple in Jerusalem, if I am not mistaken. So, in John, when Jesus is talking to the Samaritan woman at the well, he refers to this practice. The Jews wouldn't allow Samaritans to do Korban, so they were keeping the Samaritans from practicing the faith. Jesus told her that it would be done differently in the future, and so it has.
With reference to the sacrifice, it is rather striking to me that Jesus is doing the same thing in principle as was done in the Temple. In the Temple, they would bring an animal to the altar, and the animal would be killed as a "sacrifice" in order to atone for one's sins. Instead of taking an animal, Jesus would take on the sin on himself, as opposed to the animal taking on the sin.
This is what is meant then, when it is said that Jesus gave his life up for us. It is the same principle as the Jews practiced with the Korban.
Even the High Priest, Caiphas, who denounced him to the Romans in order to have him crucified, echoed the principle... See Gospel of John 11:50. (1:39 into video)
But instead of saving a nation, Jesus meant all people, as he told the woman at the well. (26 minutes into video)
So that is what it means. Actually, Korban is defined differently than sacrifice. That's because it has some negative connotations these days. It means "draw closer to God". How is what Jesus did that is any different, other than himself in place of an animal?