After the beast was killed, and the parts of it divided, the priest was to put the parts mentioned into the hands of the offerer. See Exodus 29:22-24. Made by fire; so called not strictly, as burnt-offerings are, because some parts of these were left for the priest, Leviticus 7:31; but more largely, because even these peace-offerings were in part, though not wholly, burnt. The breast may be waved to and fro by his hands, which were supported and directed by the hands of the priest.
Related Commentaries of Leviticus 7:30
Leviticus 7:30
30 His own hands shall bring the offerings of the LORD made by fire, the fat with the breast, it shall he bring, that the breast may be waved for a wave offering before the LORD.