Jamieson, Fausset and Brown on Leviticus 4:3

Le 4:3-35. Sin Offering for the Priest.

3. If the priest that is anointed do sin--that is, the high priest, in whom, considering his character as typical mediator, and his exalted office, the people had the deepest interest; and whose transgression of any part of the divine law, therefore, whether done unconsciously or heedlessly, was a very serious offense, both as regarded himself individually, and the influence of his example. He is the person principally meant, though the common order of the priesthood was included.

according to the sin of the people--that is, bring guilt on the people. He was to take a young bullock (the age and sex being expressly mentioned), and having killed it according to the form prescribed for the burnt offerings, he was to take it into the holy place and sprinkle the atoning blood seven times before the veil, and tip with the crimson fluid the horns of the golden altar of incense, on his way to the court of the priests,--a solemn ceremonial appointed only for very grave and heinous offenses, and which betokened that his sin, though done in ignorance, had vitiated all his services; nor could any official duty he engaged in be beneficial either to himself or the people, unless it were atoned for by blood.