The Lord spoke to Moses, saying, “Take Aaron and his sons with him, and the garments and the anointing oil and the bull of the sin offering and the two rams and the basket of unleavened bread. And assemble all the congregation at the entrance of the tent of meeting.” And Moses did as the Lord commanded him, and the congregation was assembled at the entrance of the tent of meeting.
The priests were consecrated to their duties in front of the entire assembly of Israel by "doing" their duties. Their immediate action upon donning priestly garments and being anointed with oil was to offer a sin offering for themselves and the nation (Leviticus 8:14). This was the beginning of a long relationship Israel had with God in which priests offered sacrifices, and regular bloody animal slaughter was the means to atone for sin. It kept them in covenant with Yahweh.
The priests were in constant demand to offer portions of each animal brought to the altar. It was a necessary duty so that sin could be dealt with and God could dwell among His people. The altar was first consecrated with blood (see Leviticus 8:15-16). It would be constantly covered in the blood of sacrifice from that point forward.
Today the blood of the Lamb of God Who takes away the sin of the world consecrates the altar of my life. Jesus was sacrificed so that I might be able to myself live as a living sacrifice. Christ has consecrated my life so that I may offer it back to God in all that I now do.