Jamieson, Fausset and Brown on Numbers 8:11-13

11-13. And Aaron shall offer the Levites--Hebrew, "as a wave offering"; and it has been thought probable that the high priest, in bringing the Levites one by one to the altar, directed them to make some simple movements of their persons, analogous to what was done at the presentation of the wave offerings before the Lord. Thus were they first devoted as an offering to God, and by Him surrendered to the priests to be employed in His service. The consecration ceremonial was repeated in the case of every Levite who was taken (as was done at a later period) to assist the priests in the tabernacle and temple. (See on 2Ch 29:34).