Leviticus 1 – 5:26
The process of sacrificing in the “mishkan” – the Tabernacle – was a complex system transferring human action symbolically to the consecrated animals. The “kohainim” the priests would sprinkle some of the blood onto the “mitzbayach” – the altar as part of the ceremony symbolizing that it should have been the sinner’s blood not the animals. It is the animal and its blood that becomes a substitution for the sins of the human. Sinful actions and sinful thoughts including sexual inappropriateness like intercourse with a woman who is menstruating can be mitigated by sacrifice.