Check out Genesis 4:1-16. The synopsis is that Cain made an offering of his harvest and Abel offered the firstlings of his flock. God accepted Abel's sacrifice, but not Cain's. Cain was jealous, killed Abel, and lied about it. God punished Cain, but His punishment was not without mercy.
What is it with sacrifice? The very first thing that we hear about after Adam and Eve get kicked out of the Garden of Eden is the offering of sacrifice to God. This is an essential part of Judaism throughout the Old Testament, as well as a key component of worship for many pagans.
But why? I don't have a straight up answer for that. All I know is that the word "sacrifice" comes from a root word that means "to make holy." They're offered to God to give Him glory and praise and to ask for mercy. I think, too, that they are a way of "putting your money where your mouth is". It appears that Cain didn't offer the best of what he had to give, which may be why God didn't accept his sacrifice. It was a way for the people of the time to put the weight of their actions behind their words. We don't make animal sacrifices anymore, but when we do make sacrifices, we tend to do it for people that we love or causes that are very important.
I know I don't fully understand sacrifices, but I think that they're very important to continue to learn about. The more we understand Judaism and Jewish sacrifice, the better we'll understand our own faith as well.
More later. Among other things I can't wait to talk about todah offerings.