In this first complete series of offerings made by the high priest, the sacrifices take their appointed order; first, the sin-offering to make atonement; then the burnt-offering, to signify the surrender of the body, soul and spirit to Yahweh in heaven; and lastly the peace-offering, to show forth the communion vouchsafed to those who are justified and sanctified. See Leviticus 8:14 note.
Leviticus 9:15-21
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.a
17 And he brought the meat offering, and tookb 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.