Leviticus 1:1-9 God explained precisely how He wanted His people to perform their sacrifices. Although this scene is foreign and perhaps repulsive to us, to them it would have been both obvious and accepted. Also, in their agrarian world, killing animals was completely commonplace. Since many more people raised livestock, they did not have our modern separation between packaged meat and living animals. Furthermore, their wealth was often tied up in their physical assets rather than currency, so offering a sheep or a bull was akin to a financial sacrifice. Even so, they had to be sure to choose an animal without blemish (22:21).
Leviticus 6:1-7 Although some of the sacrifices were to show gratitude, others were to atone for sinful behavior. For example, a thief had to pay back what he stole plus twenty percent as well as offer a ram for a guilt offering to God.
Leviticus 11:1-3, 12, 20-21, 44-45 Cleanness was an important concept that extended to several areas of life, including what kinds of animals were permitted for food. God never explained His reasoning for these particular prohibitions, but many probably had to do with health.
Leviticus 15:31 Further reasons for uncleanness included giving birth (12), having a rash (13), touching certain dead animals (11:31-32), touching a corpse (21:1-3), discharging certain bodily fluids (15).
Leviticus 19:1-2, 17-18 God was also interested in moral holiness including sexual behavior (18), honoring parents (19:3), keeping Sabbaths (19:3), abstaining from idolatry (19:4), providing for the poor (19:9-10; 25:35-55), honesty (19:11-12), employment equity (19:13), fair treatment of the disabled (19:14), just courts (19:15), kind treatment of neighbors (19:16-18), child sacrifice (20:1-5), talking to the dead (20:6), harming others (24:17-22), keeping vows (27:1-13), and much more (19:19-37).
Leviticus 20:22-26; 22:31-33 God wanted His people to be different than the nations. They were to be holy to Him--His special people. He gave them special weekly, monthly, and annual times for rest and feasting (23). Additionally, He set aside one day each year for national repentance, fasting, and forgiveness (16). God wanted to dwell among His people. This is why they needed to be holy (26:11-13).
Leviticus 21:6 God instated stricter rules for priests because they came closest to the holy place, including no burying the dead except for close relatives, mourning limitations, marriage limitations, harsher penalties for children, no loose hair, and no tearing clothes. Furthermore, if a priest had any physical blemish or disability, he could not draw near and enter the tent (21:16-24).