The Sin Offering expiated (paid the debt in full) the worshipper’s unintentional weaknesses and failures before the Lord. Lev 4:1-4 (NKJV)
Each class of people had various ordinances to perform:
Sins of the high priest required the offering of a bull and the blood was not poured on the altar but sprinkled from the finger of the high priest 7 times on the altar. Then the fat was burnt, and the remainder was burned (never eaten) outside the camp “unto a clean place” where the sacrifice was made and the ashes were poured out. Lev 4:12 (NKJV)
Sins of the leaders required the offering of a male goat. The blood was sprinkled only once and the remainder was poured around the altar as with the burnt offering.
Sins of the common Israelites required female animals, goats, lambs, turtledoves, or pigeons and in the case of the very poor an offering of grain was acceptable just like a meal offering.
Unintentional sins were difficult to identify and could happen at any time and therefore the priests worked closely as mediators with God and the people and were there to instruct the people as they sought the Lord. In case any sins were not brought before the Lord there were offerings for the nation and for the high priest which covered them all in a collective way. On the Day of Atonement (Yom Kippur) the high priest sprinkled blood on the mercy seat for his own sins and the sins of the nation.