Leviticus shows us how an unholy people can worship a Holy God. The book lays out the 5 offerings and 7 feasts that show the people how to worship. Ultimately, the book, the feasts, and the laws point to Jesus.
5 Offerings: Burnt, Meal, Peace, Sin, and Trespassing
7 Feasts: Passover, Unleavened Bread, First Fruits, Pentecost, Trumpets, Day of Atonement, and Tabernacles
There are 3 types of laws:
Civil - How to set up and govern Israel
Ceremonial - How to offer sacrifices
Moral - How we live
Jesus fulfilled the first two in His coming, and the Moral law is how we continue to live out life today. He is saying, "This is who I am, reflect me, and love that way!"
We see that there is no forgiveness of sin without blood sacrifice.
We see in the Feast of Atonement (Lev 10) that God was very specific in how the people were to approach Him. Aaron's sons were cavalier in their approach, and God struck them dead on the spot.
The Day of Atonement happened one day/year. Atonement means, "covering", and this day included a "scapegoat" that had the sins of the people "placed" on it and taken out to the wilderness.
Ultimately, we see Jesus as the true substitutionary atonement. Because of His sacrifice, we can approach God personally. We are called Holy Ones. We are saints. We are covered by the blood of Jesus, and we are called to live a holy life to a world that desperately needs the ultimate sacrifice of Jesus to cover their lives.