Exodus 29:10Meaning & Commentary from the Church Fathers

Why did the priests perform the act of laying their hands on the sacrifice? They only laid their hands on certain offerings, particularly those made for atonement, rather than on all sacrifices. In contrast, for other offerings, they laid their hands upon the individuals presenting them. This practice symbolized that the sacrifice served as a substitute for the individual making the offering, and it was on behalf of that person that the sacrifice was accepted.

The text regarding the sin offering for a priest is outlined distinctly; similar to the other sin offerings for the entire congregation, it is unique in that the blood of the animal was taken into the holy place and applied to the horns of the altar of incense, unlike other sacrifices that were presented at the altar of burnt offerings. The practice of placing hands on the head of the offering is a standard procedure for all types of sacrifices.