A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
lev 4:2SIN OFFERING OF IGNORANCE. (Lev 4:1-2)
If a soul shall sin through ignorance against any of the commandments of the Lord--a soul--an individual. All sins may be considered, in a certain sense, as committed "through ignorance," error, or misapprehension of one's true interests. The sins, however, referred to in this law were unintentional violations of the ceremonial laws,--breaches made through haste, or inadvertency of some negative precepts, which, if done knowingly and wilfully, would have involved a capital punishment.
do against any of them--To bring out the meaning, it is necessary to supply, "he shall bring a sin offering."
lev 4:3SIN OFFERING FOR THE PRIEST. (Lev. 4:3-35)
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.
lev 4:11the skin of the bullock, and all his flesh--In ordinary circumstances, these were perquisites of the priests. But in the expiation necessary for a sin of the high priest, after the fat of the sacrifice was offered on the altar, the carcass was carried without the camp [Lev 4:12], in order that the total combustion of it in the place of ashes might the more strikingly indicate the enormity of the transgression, and the horror with which he regarded it (compare Heb 13:12-13).
lev 4:13if the whole congregation of Israel sin through ignorance--In consequence of some culpable neglect or misapprehension of the law, the people might contract national guilt, and then national expiation was necessary. The same sacrifice was to be offered as in the former case, but with this difference in the ceremonial, that the elders or heads of the tribes, as representing the people and being the principal aggressors in misleading the congregation, laid their hands on the head of the victim. The priest then took the blood into the holy place, where, after dipping his finger in it seven times, he sprinkled the drops seven times before the veil. This done, he returned to the court of the priests, and ascending the altar, put some portion upon its horns; then he poured it out at the foot of the altar. The fat was the only part of the animal which was offered on the altar; for the carcass, with its appurtenances and offals, was carried without the camp, into the place where the ashes were deposited, and there consumed with fire.
lev 4:22When a ruler hath sinned, and done somewhat through ignorance against any of the commandments--Whatever was the form of government, the king, judge, or subordinate, was the party concerned in this law. The trespass of such a civil functionary being less serious in its character and consequences than that either of the high priest or the congregation, a sin offering of inferior value was required--"a kid of the goats"; and neither was the blood carried into the sanctuary, but applied only to the altar of burnt offering; nor was the carcass taken without the camp; it was eaten by the priests-in-waiting.
lev 4:27if any one of the common people sin through ignorance--In this case the expiatory offering appointed was a female kid, or a ewe-lamb without blemish; and the ceremonies were exactly the same as those observed in the case of the offending ruler [Lev 4:22-26]. In these two latter instances, the blood of the sin offering was applied to the altar of burnt offering--the place where bloody sacrifices were appointed to be immolated. But the transgression of a high priest, or of the whole congregation, entailing a general taint on the ritual of the tabernacle, and vitiating its services, required a further expiation; and therefore, in these cases, the blood of the sin offering was applied to the altar of incense [Lev 4:6, Lev 4:17].
lev 4:35it shall be forgiven him--None of these sacrifices possessed any intrinsic value sufficient to free the conscience of the sinner from the pollution of guilt, or to obtain his pardon from God; but they gave a formal deliverance from a secular penalty (Heb 9:13-14); and they were figurative representations of the full and perfect sin offering which was to be made by Christ.