15 And he brought the people’s offering, and took the goat, which was the sin offering for the people, and slew it, and offered it for sin, as the first.
16 And he brought the burnt offering, and offered it according to the manner.
17 And he brought the meat offering, and took an handful thereof, and burnt it upon the altar, beside the burnt sacrifice of the morning.
18 He slew also the bullock and the ram for a sacrifice of peace offerings, which was for the people: and Aaron’s sons presented unto him the blood, which he sprinkled upon the altar round about,
19 And the fat of the bullock and of the ram, the rump, and that which covereth the inwards, and the kidneys, and the caul above the liver:
20 And they put the fat upon the breasts, and he burnt the fat upon the altar:
21 And the breasts and the right shoulder Aaron waved for a wave offering before the Lord; as Moses commanded.
22 And Aaron lifted up his hand toward the people, and blessed them, and came down from offering of the sin offering, and the burnt offering, and peace offerings.
In the last section Aaron performed the offerings for himself, with the help of his sons, and next he performed the offerings for the general population of Israel. Once again, his sons assisted by presenting the blood for sprinkling. Now, at last, everyone had been sanctified. Everyone had been committed to the Lord.
Admittedly, Moses was perhaps an outlier in this moment. I suppose he could be considered part of the body of Israel, a subject of this general offering that Aaron just completed. On the other hand, we could definitely say that his sanctification and purification had already transpired during one of his visits to the mountain. He did appear once with a shining face after all, which sounds pretty sanctified! Thus, by one way or another, Moses, Aaron, the priests, and all the Israelites were now one in God.
Aaron commemorated this moment by pronouncing a blessing upon the people. We do not read the words that he said, but this further shows the fatherly relationship he had to the great Israelite family.