Imagine that you are an Israelite, following with Moses God's pillar of cloud by day and fire by night through the desert. You have a small herd of goats. Moses comes down from the mountain (the second time -- you thankfully survived the cleansing of the camp after that debacle with the golden calf). He reports all the things that God has said you were to no longer do. You're pretty sure you can manage it...at least most of them. Well, some of them. You're going to give it a try.
Then Moses announces that if you commit a sin, even unintentionally, when you realize that you've sinned or when someone points out your sin, you must make a sin offering to atone for the wrong you've committed against God. Then Moses begins to describe how this sin offering must be made. He says that you must look over your herd and pick your very best female goat, one that is without any sort of defect. You must bring it to the tabernacle, place your hand on its head and kill it. Then you must sprinkle its blood on the altar and burn on the altar the fat and entrails - but the meat and the hide, the parts of the animal that are the most useful, you must carry outside the camp and incinerate. You must take the very best that you have and burn it up -- that part isn't even the offering, it's just burnt up like garbage.
It's hard to put this in a modern context because most of us don't raise goats. But think about the dependence that the Israelites had upon their flocks. The female goats needed for this sacrifice provided milk, were bred to increase their herd, their meat could be eaten and their skins used for clothes, but all of these uses were lost when the animal was sacrificed. Depending on the size of your herd, if you had trouble keeping the commandments, you could find yourself without any resource for supporting your family pretty quickly.
How seriously do we take the commands of God? Would we take them as lightly if we knew that failure to obey them could leave us penniless without any means of income? How often do we confess and repent -- only to return to the same sin? It was never God's intent that these sacrifices be a kind of ancient indulgence, a sin tax paid to allow us to go on with our sin. The sacrifices were meant to "hit home," to illustrate the destructive nature of sin.