The word "Leviticus" means "pertaining to the Levites". As such, it contains the System of Laws, administered by the Levitical Priesthood, under which the Hebrew nation lived. These laws were given mostly at Mount Sinai, with additions, repetitions, and explanations throughout the wandering of the Israelites in the wilderness.
The Levites, one of the Twelve Tribes, were set apart for the work of God. God took them, in lieu of First-Born sons. God claimed the First-Born, both of men and flocks. They were supported by Tithes; and had 48 cities (Numbers 35:7; Joshua 21:19).
One family of Levites, Aaron and his sons, were set apart to be Priests. The rest of the Levites were to be assistants to the Priests. Their duties were the care of the Tabernacle (and later, the Temple); and to be Teachers, Scribes, Musicians, Officers, and Judges. (See 1 Chronicles 23.)