Every year as we begin Leviticus, we cannot help being impressed by the emphasis on blood in the Tabernacle worship service. Many New Testament churches treat Leviticus as a vaguely embarrassing throwback to a more primitave time which we have outgrown. Nothing could be farther from the truth.
The word 'sacrifice' is in some ways an unfortunate translation of the Hebrew 'korban'. In modern usage, its primary connotation is giving something up. While it is true that an offering must be something of value which one gives up, that describes the process and not the purpose. In other words, many of us view sacrifice in the same way we view the fine in a traffic court - having sinned, we need to pay the judgment.
This attitude misses the whole point. The root of 'korban', 'brk' in Hebrew means to bring near or to draw near. That is to say that the sacrifice is intended to draw one near to God. It is not and never has been a bribe to keep an angry God off of one's case.
To what are we drawing near? It is significant that He uses the name 'YHVH' in this section of the Torah rather than 'Elohim'. YHVH is the name he uses to denote His desire for relationship and mercy, not for judgement.
If we believe that drawing close to God will effect a change in us, the purpose of the korban becomes clear. To bring a sacrifice should be to draw near to Him in anticipation that He will change us from what we were into what He wants us to become.
We see this concept of drawing near with respect to Messiah's blood in the New Testament. For example, "But now in Christ Jesus you who once were far off have been brought near by the blood of Christ."(Eph 2:13). The idea being that through His sacrifice we may draw near to the commonwealth of Israel and near to God. The clear message in the rest of Ephesians is that this drawing near is expected to change us.
Unfortunately, many people simply want to 'get the fine paid' and get out of court. For them, there is no drawing near and no essential change. They are sinners before the sacrifice and remain so afterwards.