The Levitical-era laws were not merely rituals. They were also about behaving honestly and responsibly. Examples:
"If any one sins in that he hears a public adjuration to testify and though he is a witness, whether he has seen or come to know the matter, yet does not speak, he shall bear his iniquity." (Leviticus 5:1 RSV)
They were also about caring for one's health. Examples:
"Or if any one touches an unclean thing, whether the carcass of an unclean beast or a carcass of unclean cattle or a carcass of unclean swarming things, and it is hidden from him, and he has become unclean, he shall be guilty. Or if he touches human uncleanness, of whatever sort the uncleanness may be with which one becomes unclean, and it is hidden from him, when he comes to know it he shall be guilty." (Leviticus 5:2-3 RSV)
The sacrifices for violations almost certainly helped the people to strive to obey; watching an innocent lamb or dove being killed for the guilt of one's self was surely an incentive to not do wrong (keeping in mind that all humans are responsible for the killing of a far more perfect and innocent "lamb" as payment for our sins - see Why Blood?).
"When a man is guilty in any of these, he shall confess the sin he has committed, and he shall bring his guilt offering to The Lord for the sin which he has committed, a female from the flock, a lamb or a goat, for a sin offering; and the priest shall make atonement for him for his sin.
Leviticus Chapter 6
All of the laws were and are based upon The Ten Commandments (see The First Commandment, The Second Commandment, The Third Commandment, The Fourth Commandment, The Fifth Commandment, The Sixth Commandment, The Seventh Commandment, The Eighth Commandment, The Ninth Commandment and The Tenth Commandment. Notice below how violators "shall bring to the priest his guilt offering to The Lord" i.e. the high priest was merely a symbol of the High Priest that actually has the power to forgive and make atonement (see What Is Jesus Christ Doing Right Now?).
"The Lord said to Moses [see The Education Of Moses], "If any one sins and commits a breach of faith against The Lord by deceiving his neighbor in a matter of deposit or security, or through robbery, or if he has oppressed his neighbor or has found what was lost and lied about it, swearing falsely - in any of all the things which men do and sin therein, when one has sinned and become guilty, he shall restore what he took by robbery, or what he got by oppression, or the deposit which was committed to him, or the lost thing which he found, or anything about which he has sworn falsely; he shall restore it in full, and shall add a fifth to it, and give it to him to whom it belongs, on the day of his guilt offering.
Leviticus Chapter 7
Only "clean" animals (see the Fact Finder question below) were acceptable for sacrifice. This principle was used in both a physical and spiritual sense.
"Flesh that touches any unclean thing shall not be eaten; it shall be burned with fire. All who are clean may eat flesh, but the person who eats of the flesh of the sacrifice of The Lord's peace offerings while an uncleanness is on him, that person shall be cut off from his people. And if any one touches an unclean thing, whether the uncleanness of man or an unclean beast or any unclean abomination, and then eats of the flesh of the sacrifice of The Lord's peace offerings, that person shall be cut off from his people."
Fact Finder: How is it that The Lord's dietary laws for humans are exactly that - laws of healthy diet for all humans? How is it that they are simply about good health, not "religion"?