As mentioned before, the blood of an animal represented the life of an animal. Pouring out the blood of an animal on the altar signified that life had been given in order to make atonement for sin. As such, the animal took the place of the worshipper so that the worshipper could be restored to the Lord.
9 and he shall sprinkle some of the blood of the sin offering on the side of the altar, while the rest of the blood shall be drained out at the base of the altar; it is a sin offering.