Smith's Bible Dictionary
Wave Offering. This rite, together with that of "heaving" or "raising" the offering, was an inseparable accompaniment of Peace Offerings. In such, the right shoulder, considered the choicest part of the victim, was to be "heaved", and viewed as holy to the Lord, only eaten, therefore, by the priest: the breast was to be "waved", and eaten by the worshipper.
The scriptural notices of these rites are to be found in Exodus 29:24; Exodus 29:28; Leviticus 7:30; Leviticus 7:34; Leviticus 8:27; Leviticus 9:21; Leviticus 10:14-15; Leviticus 23:10; Leviticus 23:15; Leviticus 23:20; Numbers 6:20; Numbers 18:11; Numbers 18:18; Numbers 18:26-29; etc.
In conjecturing the meaning of this rite, regard must be had that, it was the accompaniment of Peace Offerings, which were witnesses to a ratified covenant - an established communion between God and man.
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Smith, William, Dr. Entry for 'Wave Offering'. Smith's Bible Dictionary. https://www.studylight.org/dictionaries/eng/sbd/w/wave-offering.html. 1901.