Leviticus is full of rules about how people should live their lives, for example what to do if you have mildew on your clothes. But how should Christians choose which of these rules are relevant to today and which to ignore? An example of one most people ignore is:
"When a woman has her monthly period, she remains unclean for seven days. Anyone who touches her is unclean until evening. Anything on which she sits or lies during her monthly period is unclean. Anyone who touches her bed or anything on which she has sat must wash his clothes and have a bath, and he remains unclean until evening" (Leviticus 15:19-24)
This is clearly impractical and is not followed by most Christians.
So how would you decide what to follow and what not to follow? Why is it that this rule does not need to be followed but others do?
Perhaps it would help to understand exactly what we mean by "Old Covenant" and "New Covenant".
In the Old Testament, God made a deal with Abraham (Abraham was acting as a sort of representative for Israel).
He told Abraham, "Here's the covenant I'm making with you: You will be My people, and I will be Your God. I will give you My law and when you follow it, you will be blessed. When you break it, you will be cursed. By following My law and allowing Me to bless you, you will become a beacon to the nations around you."
Think of it as God's first evangelism plan. The surrounding nations would see how good and merciful God was to Israel and say to themselves, "I don't know who their God is, but He sure beats [insert pagan god here]."
There were different kinds of laws.
Some, such as the Ten Commandments, were axiomatic. They were given across the board, to all people for all time. One of the ways that we know these laws were not limited to the Old Covenant is that they're repeated in the New Testament, which is the New Covenant.
Others, such as the ones I'm sure you've heard about not trimming the corners of your beard, or not wearing two kinds of fabric, were laws specifically to Israel, so that they would remain seperate and undefiled from pagan religions. Pagan priests in neighboring countries identified themselves by their vestments and these included the vestments made of the two fabrics, and the unique facial hair, just as some sects today do this. It isn't a bad thing, in and of itself, but God did not want His children identified with His enemies.
Now, some laws, such as the Sabbath and certain feast obligations served a very important purpose. The Bible tells us in Colossians 2 (I think) that these laws were a foreshadowing of the coming Messiah, Jesus, and the rest we would have in Him.
The passage in Colossians goes on to tell us that these things were a foreshadowing of Christ, but now that Christ has come, we no longer need the foreshadow, because we have the real thing.
This to me is one of the most fascinating things about the OT. Christ is everywhere in the OT.
There were other laws, which were ceremonial laws and preistly laws. These dictated who could come before God and how they were to do it.
In the temple, the inner sanctuary of the temple was called the "Holy of Holies". This was the place where God dwelt among the Israelites and it was considered to be so sacred that only consecrated, ritually prepared priests could enter it. It was so sacred that it was surrounded by a large veil and this veil was wrapped around it several times to form a kind of maze through which the priest had to walk.
Once a year, on Yom Kippur, the priest would enter the Holy of Holies, make the sacrifice and pray for the forgiveness of his people.
But then the Bible tells us that when Jesus was crucified, this veil in the temple in Jerusalem ripped in half by an act of God.
What this symbolized was the end of this priestly system and the beginning of the ability of God's people to approach Him directly, through Jesus Christ.
With the passing of this temple custom, the ceremonial and priestly laws also passed away and the Old Covenant became the New Covenant.
Probably much more than you wanted to know, but I hope that helps.