C. F. Keil and Franz Delitzsch on Numbers 8:11

Num 8:11

This transfer was to be completed by Aaron’s waving the Levites as a wave-offering before Jehovah on behalf of the children of Israel, i.e., by his offering them symbolically to the Lord as a sacrifice presented on the part of the Israelites. The ceremony of waving consisted no doubt in his conducting the Levites solemnly up to the altar, and then back again. On the signification of the verb, see at Lev 7:30. The design of the waving is given in Num 8:11, viz., “that they might be to perform the service of Jehovah” (Num 8:24-26 compared with Num 4:4-33).