The wave offering and heave offering before the Lord
Archimandrite Nikifor’s Biblical Encyclopedia
(Exod. 29:24–28, and elsewhere) — ritual acts of the offering and consecration of a sacrifice to God; with the latter ritual act was combined the waving of the sacrificial portions before the Lord, especially in peace offerings, or offerings of salvation, and at the consecration of priests (Exod. 29:24; Lev. 8:27). The same waving was performed at the offering of the first sheaf on the second day of Passover (Lev. 23:11), of the two lambs, and of the first fruits offered at Pentecost (Lev. 23:20).
The rite itself consisted, according to the Talmudists’ explanation, of a cross-shaped movement of the gift consecrated to God, back and forth, left and right, in the direction of the Holy of Holies. However, Holy Scripture does not speak of this directly. Sometimes the priest took the offering into his own hands and lifted it up directly before the Lord (Num. 5:25); sometimes he placed the sacrificial offering upon the hands of the one offering it and, placing his own hand beneath, performed the waving. Thus it was done by Moses at the consecration of the priests (Exod. 29:24); thus it was also done at the consecration of Nazirites (Num. 6:19, 20).