Part of the ritual of sacrifices. The person making the offering extended his hands on which the priest placed the offering and then put his hands underneath, and together they were raised up to the Lord (Exod. 29: 24). The breast of the animal was waved (swung) to and fro in the direction of the altar (Exod. 29: 26).
Similar rituals were practised by Nazirites when they made their vow of abstinence. The offering, in this case, was a ram's shoulder.
The priests received as their dues the more generous share of the wave offering (Lev. 7: 34).