How did Jesus sacrifice for us?

Jesus' sacrifice - the death on the cross - was a sacrifice for all of humankind. In order to explain how it was (and is) a sacrifice, it is necessary to go back to the beginning.

In the beginning, when God created the world, and all living things (including man and animal) it was very good (Gen. 1 and 2). He gave a commandment to the first man (Adam) and woman (Eve): "You are free to eat from any tree in the garden; but you must not eat from the tree of the knowledge of good and evil, for when you eat of it you will surely die (Gen. 2:16-17)." But Adam and Eve ate of the fruit anyway (Gen 3:1-13) and were cursed because they had not obeyed the one command from God (Gen 3:14-19). The first murder occurred shortly after (Gen. 4:6-8). Following generations were so sinful that God was grieved over the fact that He had made them (Gen. 6:7).

There were (and still are) no untainted people (Romans 1:18-32). No person or nation could attain righteousness on their own (Romans 3:23 and 4:1-24), not even Israel with the Old Testament Law (Romans 2:17-29 and 3:9).

So here we have all humanity wallowing in sin with no hope of redemption from sin and eternal life with God. End or story, right? Wrong. God, being the God of love that He is (John 3:16), provided the only way of salvation: Jesus Christ (John 3:16). By Jesus' death, his ultimate sacrifice, those who chose to believe and have faith in Him are saved from eternal death and sin (John 3:16 and Romans 4:18-25 and Romans 5:1-2).

Summery: The price for sin (which all people are under) is death. Jesus sacrificed for us by dying on the cross (Matthew 27:32-54) in our place, and opening the gate to salvation (i.e. eternity with God, freedom from sin being the monarch in our lives). Thanks God for your awesome grace!

P.S. For anyone that wishes to look up verse references used above, I suggest biblegateway.com. For futher study, try the Gospels and Romans.