The Book of Leviticus takes its name from the tribe of Levi. Moses and his brother Aaron were Levites. Aaron and his sons were chosen by God to serve as priests, to lead the worship and to offer sacrifices on behalf of the people. The other members of the tribe of Levi were appointed as assistants and (at the time of King Solomon) as Temple servants. Leviticus continues the account of the giving of the Law in Exodus, with instructions for the conduct of worship. The early Jewish Rabbis referred to Leviticus as "the Priests' Manual".
Chapters 1-7 give instructions for how to perform sacrifices. Chapters 8-10 lay down the rituals for the consecration of Priests. Chapters 11-15 give guidelines for ritual cleanliness and the distinctions between clean and unclean. Chapters 17-26 are referred to as "The Holiness Code", laws governing Israel as a holy people consecrated to God. Chapter 27 describes religious vows that people may choose to make.

Leviticus, chapters 11-15 - the rules for ritual cleanliness were not only ways of showing one's obedience to God, but were also generally good for the well-being and hygeine of the people.
Leviticus 11:3 - "chew the cud" refers to the way in which cows and other "ruminants" (cud-chewers) first swallow grass and then send it, not directly to the stomach but to an internal sac called the rumen. Then when they are resting or lying down they pull the grass back into their mouths and chew it before swallowing it properly and sending it to the stomach. The partially chewed grass which the cow chews for a second time is called the cud. So when you see pictures of cows lying down and chewing contentedly on something - they are chewing the cud.
"part the hoof", "cloven-footed" describes an animal's hoof, such as that of the cow, which is split into two parts.
Leviticus 20:2 - "give his seed to Molech" means to sacrifice his child as a burnt offerring to Molech, the god of the Ammonites