Aaron and his sons were atoned for, consecrated, and anointed as they began their priestly duties.
For the Levitical priesthood to be acceptable to GOD, it first had to be properly initiated. We previously observed that Aaron and his sons were washed and then dressed in the priestly garments.
Several additional measures were necessary before initiation was completed.
In Leviticus 8, we read:
14 Then [Moses] brought the young bull for the sin offering; and Aaron and his sons put their hands on the head of the bull for the sin offering, 15 and Moses killed it. Then he took the blood, and put some on the horns of the altar all around with his finger, and purified the altar. He poured the blood at the base of the altar, and sanctified it, to make atonement upon it. 16 Moses then took all the fat on the entrails, the fatty lobe attached to the liver, and the two kidneys with their fat, and Moses offered them on the altar. 17 But the young bull, its hide, its flesh, and its offal he burned with fire outside the camp, as the Lord commanded Moses.
18 Next, Moses brought the ram as the burnt offering. Aaron and his sons put their hands on the head of the ram, 19 and Moses killed the ram. Then he poured the blood all around on the altar 20 and cut the ram into pieces; and he offered the head, the pieces, and the fat. 21 Then he washed the stomach and the feet in water and offered the whole ram on the altar. It was a whole burnt offering for a sweet aroma, a burnt offering to the Lord, as the Lord commanded Moses.
(Leviticus 8:14-21 OSB)
The bull sin offering was for atonement, first for the altar and second for Aaron and his sons, the priests.
The Greek word that is translated atonement is ἱλάσκομαι (hilaskomai). This word means a propitiation, which is the idea of winning the favor someone by doing something that pleases them.
It carries the idea of a covering over, such as a wrong (ex: sin).
Before any sinner can serve as a priest of GOD, there must first be an atoning sacrifice offered for them.
22 After this, Moses brought the second ram, the ram of consecration. Then Aaron and his sons put their hands on the head of the ram, 23 and Moses killed it. Also he took some of its blood and put it on the tip of Aaron's right ear, on the thumb of his right hand, and on the big toe of his right foot. 24 Then Moses brought Aaron's sons; and he put some of the blood on the tips of their right ears, on the thumbs of their right hands, and on the big toes of their right feet. Then he poured the blood all around on the altar. 25 He took the fat and the fat tail, all the fat on the entrails, the fatty lobe attached to the liver, the two kidneys and their fat, and the right thigh; 26 and from the basket of consecration before the Lord, he took one unleavened cake, a cake of bread anointed with oil, and one wafer and put them on the fat and on the right thigh; 27 and he put all these in Aaron's hands and in his sons’ hands and offered them as a choice portion before the Lord. 28 Then Moses took them from their hands and offered them on the altar for a whole burnt offering of consecration, which was a sweet aroma and a burnt offering to the Lord. 29 Moses also took the breast and removed it as a deposit from the ram of consecration before the Lord. It was Moses’ part, as the Lord commanded Moses.
(Leviticus 8:22-29 OSB)
Consecration is a synonym for sanctification. It is the Greek word ἁγιάζω (hagiazó), which means "to make holy, consecrate, sanctify."
Consecration carries the idea of setting apart from that which is common, profane, or impure.
It was important to GOD that Israel—both the priests and the common people—appreciated the weightiness of serving as intermediaries to GOD on their behalf. This was a special assignment that was to be undertaken seriously and to be respected among the nation.
30 Moses then took some of the anointing oil and some of the blood on the altar and sprinkled it on Aaron and his garments, and on his sons and their garments with him; and he sanctified Aaron and his garments, and his sons and their garments with him.
31 After this, Moses said to Aaron and his sons, “Boil the flesh in the court of the tabernacle of testimony, in a holy place, and eat it there with the bread in the basket of consecration as I was commanded, saying, ‘Aaron and his sons shall eat it.’ 32 What remains of the flesh and the bread shall be burned with fire. 33 You shall not go outside the door of the tabernacle of testimony for seven days, until the days of your consecration are fulfilled. For seven days he shall consecrate you. 34 As the Lord did on this day, He commanded to do to make atonement for you. 35 Therefore you shall stay at the door of the tabernacle of testimony day and night for seven days and keep the charge of the Lord, that you may not die; for the Lord God so commanded me.” 36 So Aaron and his sons did all the words the Lord commanded Moses.
(Leviticus 8:30-36 OSB)
Lastly, Moses anointed Aaron and his sons with oil. They ate the prescribed meal and entered the tabernacle where they remained for a week, not to exit under penalty of death.
All of this should give us a great appreciation for the seriousness of the role of the priesthood.