Jamieson, Fausset and Brown on Deuteronomy 18:3

3. this shall be the priest's due from the people--All who offered sacrifices of thanksgiving or peace offerings (Le 7:31-33) were ordered to give the breast and shoulder as perquisites to the priests. Here "the two cheeks" or head and "the maw" or stomach, deemed anciently a great dainty, are specified. But whether this is a new injunction, or a repetition of the old with the supplement of more details, it is not easy to determine.