Leviticus is often very boring, at times horrifying, and at certain rare moments satisfying. And that's no wonder: it's an ancient document about government. After the story of the Exodus, in which God leads the nation of Israel out of Egypt, declares them his people, and makes a covenant with them to be their king, a question remains: what is God's administration going to be like? There's no separation of church and state here; the priests are the ones who provide access to God, the king of Israel.
Caveat: Moses is not himself a priest, yet he is higher than all of them. The refrain of Leviticus is, "The Lord spoke to Moses, saying..." Although the priests are to minister more directly to God than the common people, there is yet a buffer even between the priests and God. The holiness of God is probably the key issue throughout all of Leviticus. Thus the writer is concerned with demonstrating how nothing tainted can come near him without following strict guidelines, not even the most holy of all the people of Israel.