Jamieson, Fausset and Brown on Leviticus 7:29-34

Le 7:28-38. The Priests' Portion.

29-34. He that offereth the sacrifice of his peace offerings unto the Lord--In order to show that the sacrifice was voluntary, the offerer was required to bring it with his own hands to the priest. The breast having been waved to and fro in a solemn manner as devoted to God, was given to the priests; it was assigned to the use of their order generally, but the right shoulder was the perquisite of the officiating priest.