The purpose for many of the purification laws are for purely sanitary reasons and much like the dietary laws, they just make good sense. 

Moses spent 40 years practicing and maintaining all the laws.  The priests would have had access all this time to Moses and Aaron if they needed clarification on any of the laws.  Praise God, we not only have the written Word of God, we have the Holy Spirit if we need clarification on anything!

The following verses show us another connection between the Old and New Testaments.

Lev 12:7-8
"'These are the regulations for the woman who gives birth to a boy or a girl. If she cannot afford a lamb, she is to bring two doves or two young pigeons, one for a burnt offering and the other for a sin offering. In this way the priest will make atonement for her, and she will be clean.'"

Luke 2:22-24
When the time of their purification according to the Law of Moses had been completed, Joseph and Mary took him to Jerusalem to present him to the Lord (as it is written in the Law of the Lord, "Every firstborn male is to be consecrated to the Lord"),and to offer a sacrifice in keeping with what is said in the Law of the Lord: "a pair of doves or two young pigeons."
The atonement offering was given by Mary for her purification after the birth of Jesus. Since they gave either two doves or two pigeons, it meant that Mary and Joseph most likely couldn’t afford a lamb.

When we read the regulations concerning uncleanness when touching a dead body during Passover, we couldn't help but think about Joseph of Arimathea and Nicodemus. Because they would have been considered unclean after touching Jesus' body, they would not be allowed to celebrate Passover at the regular time.

After reading about all the rules and regulations for leprosy cleansing in Lev 14, it adds a whole new dimension to the story in Luke about the ten lepers who were healed by Jesus. All Jesus said to them was “Go, show yourselves to the priests.” It sure involved a whole lot more than just making an appearance.

Luke 17:12-14
As he was going into a village, ten men who had leprosy met him. They stood at a distance and called out in a loud voice, "Jesus, Master, have pity on us!" When he saw them, he said, "Go, show yourselves to the priests." And as they went, they were cleansed.

An even greater message for us is found in the last part of verse 14... "And as they went, they were cleansed." The lepers were cleansed, as they went. It truly was an ACT of faith on their part. When Jesus cleanses us from our sins, it is up to us to ACT and remove ourselves from our life of sin. Remember the Hebrew word picture for repent is "to burn the house".