Albert Barnes Commentary Deuteronomy 18:3

"And this shall be the priests` due from the people, from them that offer a sacrifice, whether it be ox or sheep, that they shall give unto the priest the shoulder, and the two cheeks, and the maw." — Deuteronomy 18:3 (ASV)

For “maw” read stomach, which was regarded as one of the richest and choicest parts. As the animal killed may be considered to consist of three principal parts, head, feet, and body, a portion of each is by this regulation to be given to the priest, thus representing the consecration of the whole; or, as some ancient commentators think, the dedication of the worshipper's words, acts, and appetites to God.

The text probably refers to peace-offerings, and animals killed for the sacrificial meals held in connection with the peace-offerings.