John Wesley on Exodus 29:22

Part of it was to be first waved before the Lord, and then burnt upon the altar, these were first put into the hands of Aaron to be waved to and fro in token of their being offered to God, and then they were to be burnt upon the altar, for the altar was to devour God's part of the sacrifice. Thus God admitted Aaron and his sons to wait at his table, taking the meat of his altar from their hands. Here, in a parenthesis as it were, comes in the law concerning the priests part of the peace - offerings afterwards, the breast and shoulder, which were now divided; Moses had the breast, and the shoulder was burnt on the altar with God's part.