For “maw” read stomach, which was regarded as one of the richest and choicest parts. As the animal slain may be considered to consist of three principal parts, head, feet, and body, a portion of each is by the regulation in question to be given to the priest, thus representing the consecration of the whole; or, as some ancient commentators think, the dedication of the words, acts, and appetites of the worshipper to God.
The text probably refers to peace-offerings, and animals killed for the sacrificial meals held in connection with the peace-offerings.