The title is the theme of the book of Leviticus. "And the LORD spoke to Aaron, saying . . . You are to distinguish between the holy and the common, and between the unclean and the clean, and you are to teach the people of Israel all the statutes that the LORD has spoken to them by Moses.” (Lev. 10:8, 10-11) The most basic job of the priests was to learn the difference between the clean and unclean and the holy and common and teach that to the people of Israel.
Everything in Leviticus relates in one way or another to this central premise. The first seven chapters detail the different types of sacrifices: how each is to be performed, which animals may be used, how they are presented to the Lord and exactly where they are to be slaughtered (some animals were presented/killed at the door of the tabernacle, others on the North side of the altar), which parts are to be burnt on the altar and which are to be eaten by the priests and/or the offeror. The same animal might be offered in different ways depending on the type of sacrifice being made. Every word of instruction for the sacrifices is about cleanliness and holiness. Sacrifices to the Lord were not to be treated casually as if all that mattered was the heart of the worshipper. They were not common, but holy. the animals used must be clean animals, but also holy: not spotted or blemished, not halt or lame, not sick.
Chapters eight through ten instruct how to consecrate the priests. The overriding emphasis here is on the holiness of their office and the absolute need to maintain their ceremonial cleanliness. So holy was the High Priest that he was not allowed to even participate in the funeral of his own father because to handle a dead body would make him unclean.
Chapters eleven through 15 enumerate the laws of cleanliness (far more involved than just which animals belonged in which category) and chapters 18-27 contain the laws of holiness. The holiness laws were different from the regular civil laws contained within the Law of Moses because the explanation of these laws was simply "I Am YHWH!" Many don't even have punishments for breaking the law just the statement that the law is basic to the character of God. Chapter eleven contains the famous command "For I am Jehovah your God: sanctify yourselves therefore, and be ye holy; for I am holy: neither shall ye defile yourselves" (vs 44) while in chapter 20 God says, "Sanctify yourselves therefore, and be ye holy; for I am Jehovah your God." (vs 7)
Finally, chapters sixteen and seventeen describe the Day of Atonement. This day was dedicated to the re-sanctification of Israel each year. Atonement was made for the nation's sins. The tabernacle was sanctified again. This day and its events were emblematic of the effort to remain clean and holy before the Lord. In like manner, the entire book of Leviticus teaches the people how to remain clean and holy and shows just what an effort that will take.
So why did I just waste your time going through all of that? The priests were to learn all these arcane rules and teach them to the people, so what? 1 Peter 2:9 "But ye are an elect race, a royal priesthood, a holy nation, a people for God's own possession, that ye may show forth the excellencies of him who called you out of darkness into his marvellous light". Just as the priests were to learn to distinguish between the clean and unclean, the holy and common and teach the people, so we, as part of Christ's new kingdom of priests, are to maintain our own holiness and proper standing before the Lord and teach the world about the expectations of God. When people ask if it really matters to act only in the manner authorized in the New Testament we can say, "Yes!" because the authorized manner is the teaching of the Lord. Just as in Leviticus, what the Lord teaches is the holy way He wants things to be done and any other way would be unholy, common. Is maintaining my sexual purity really that important? Yes, because we are to be holy, not commonly had by all in the world. Our speech is to be clean, not vulgar, because we are the priests of God and the first responsibility of priests, even before teaching the people, was to maintain their own holiness. Then, while maintaining our cleanliness before the Lord, we spread across the world His word, showing forth His excellencies.
Psalms 24:3-5 "Who shall ascend into the hill of Jehovah? And who shall stand in his holy place? He that hath clean hands, and a pure heart; Who hath not lifted up his soul unto falsehood, And hath not sworn deceitfully. He shall receive a blessing from Jehovah, And righteousness from the God of his salvation."