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 16:1HOW THE HIGH PRIEST MUST ENTER INTO THE HOLY PLACE. (Lev. 16:1-34)
after the death of the two sons of Aaron, when they offered before the Lord, and died--It is thought by some that this chapter has been transposed out of its right place in the sacred record, which was immediately after the narrative of the deaths of Nadab and Abihu [Lev. 10:1-20]. That appalling catastrophe must have filled Aaron with painful apprehensions lest the guilt of these two sons might be entailed on his house, or that other members of his family might share the same fate by some irregularities or defects in the discharge of their sacred functions. And, therefore, this law was established, by the due observance of whose requirements the Aaronic order would be securely maintained and accepted in the priesthood.
lev 16:2Speak unto Aaron thy brother, that he come not at all times into the holy place within the veil, &c.--Common priests went every day into the part of the sanctuary without the veil to burn incense on the golden altar. But none except the high priest was allowed to enter within the veil, and that only once a year with the greatest care and solemnity. This arrangement was evidently designed to inspire a reverence for the most holy place, and the precaution was necessary at a time when the presence of God was indicated by sensible symbols, the impression of which might have been diminished or lost by daily and familiar observation.
I will appear in the cloud--that is, the smoke of the incense which the high priest burnt on his yearly entrance into the most holy place: and this was the cloud which at that time covered the mercy seat.
lev 16:3Thus shall Aaron come into the holy place--As the duties of the great day of atonement led to the nearest and most solemn approach to God, the directions as to the proper course to be followed were minute and special.
with a young bullock . . . and a ram--These victims he brought alive, but they were not offered in sacrifice till he had gone through the ceremonies described between Lev 16:3-11. He was not to attire himself on that occasion in the splendid robes that were proper to his sacred office, but in a plain dress of linen, like the common Levites, for, as he was then to make atonement for his own sins, as well as for those of the people, he was to appear in the humble character of a suppliant. That plain dress was more in harmony with a season of humiliation (as well as lighter and more convenient for the duties which on that occasion he had singly to perform) than the gorgeous robes of the pontificate. It showed that when all appeared as sinners, the highest and lowest were then on a level, and that there is no distinction of persons with God [Act 10:34].
lev 16:5shall take of the congregation . . . two kids of the goats . . . and one ram--The sacrifices were to be offered by the high priest, respectively for himself and the other priests, as well as for the people. The bullock (Lev 16:3) and the goats were for sin offerings and the rams for burnt offerings. The goats, though used in different ways, constituted only one offering. They were both presented before the Lord, and the disposal of them determined by lot, which Jewish writers have thus described: The priest, placing one of the goats on his right hand and the other on his left, took his station by the altar, and cast into an urn two pieces of gold exactly similar, inscribed, the one with the words "for the Lord," and the other for "Azazel" (the scapegoat). After having well shaken them together, he put both his hands into the box and took up a lot in each: that in his right hand he put on the head of the goat which stood on his right, and that in his left he dropped on the other. In this manner the fate of each was decided.
lev 16:11Aaron shall bring the bullock of the sin offering which is for himself, &c.--The first part of the service was designed to solemnize his own mind, as well as the minds of the people, by offering the sacrifices for their sins. The sin offerings being slain had the sins of the offerer judicially transferred to them by the imputation of his hands on their head (Lev 4:4, Lev 4:15, Lev 4:24, Lev 4:29, Lev 4:33); and thus the young bullock, which was to make atonement for himself and the other priests (called "his house," Psa 135:19), was killed by the hands of the high priest. While the blood of the victim was being received into a vessel, taking a censer of live coals in his right hand and a platter of sweet incense in his left, he, amid the solemn attention and the anxious prayers of the assembled multitude, crossed the porch and the holy place, opened the outer veil which led into the holy of holies and then the inner veil. Standing before the ark, he deposited the censer of coals on the floor, emptied the plate of incense into his hand, poured it on the burning coals; and the apartment was filled with fragrant smoke, intended, according to Jewish writers, to prevent any presumptuous gazer prying too curiously into the form of the mercy seat, which was the Lord's throne. The high priest having done this, perfumed the sanctuary, returned to the door, took the blood of the slain bullock, and, carrying it into the holy of holies, sprinkled it with his finger once upon the mercy seat "eastward"--that is, on the side next to himself; and seven times "before the mercy seat"--that is, on the front of the ark. Leaving the coals and the incense burning, he went out a second time, to sacrifice at the altar of burnt offering the goat which had been assigned as a sin offering for the people; and carrying its blood into the holy of holies, he made similar sprinklings as he had done before with the blood of the bullock. While the high priest was thus engaged in the most holy place, none of the ordinary priests were allowed to remain within the precincts of the tabernacle. The sanctuary or holy place and the altar of burnt offering were in like manner sprinkled seven times with the blood of the bullock and the goat. The object of this solemn ceremonial was to impress the minds of the Israelites with the conviction that the whole tabernacle was stained by the sins of a guilty people, that by their sins they had forfeited the privileges of the divine presence and worship, and that an atonement had to be made as the condition of God's remaining with them. The sins and shortcomings of the past year having polluted the sacred edifice, the expiation required to be annually renewed. The exclusion of the priests indicated their unworthiness and the impurities of their service. The mingled blood of the two victims being sprinkled on the horns of the altar indicated that the priests and the people equally needed an atonement for their sins. But the sanctuary being thus ceremonially purified, and the people of Israel reconciled by the blood of the consecrated victim, the Lord continued to dwell in the midst of them, and to honor them with His gracious presence.
lev 16:20he shall bring the live goat--Having already been presented before the Lord (Lev 16:10), it was now brought forward to the high priest, who, placing his hands upon its head, and "having confessed over it all the iniquities of the people of Israel, and all their transgressions in all their sins," transferred them by this act to the goat as their substitute. It was then delivered into the hands of a person, who was appointed to lead him away into a distant, solitary, and desert place, where in early times he was let go, to escape for his life; but in the time of Christ, he was carried to a high rock twelve miles from Jerusalem, and there, being thrust over the precipice, he was killed. Commentators have differed widely in their opinions about the character and purpose of this part of the ceremonial; some considering the word "Azazel," with the Septuagint and our translators, to mean, "the scapegoat"; others, "a lofty, precipitous rock" [BOCHART]; others, "a thing separated to God" [EWALD, THOLUCK]; while others think it designates Satan [GESENIUS, HENGSTENBERG]. This last view is grounded on the idea of both goats forming one and the same sacrifice of atonement, and it is supported by Zac 3:1-10, which presents a striking commentary on this passage. Whether there was in this peculiar ceremony any reference to an Egyptian superstition about Typhon, the spirit of evil, inhabiting the wilderness, and the design was to ridicule it by sending a cursed animal into his gloomy dominions, it is impossible to say. The subject is involved in much obscurity. But in any view there seems to be a typical reference to Christ who bore away our sins [Heb 10:4; Jo1 3:5].
lev 16:23Aaron shall come into the tabernacle of the congregation, and shall put off the linen garments--On the dismissal of the scapegoat, the high priest prepared for the important parts of the service which still remained; and for the performance of these he laid aside his plain linen clothes, and, having bathed himself in water, he assumed his pontifical dress. Thus gorgeously attired, he went to present the burnt offerings which were prescribed for himself and the people, consisting of the two rams which had been brought with the sin offerings, but reserved till now. The fat was ordered to be burnt upon the altar; the rest of the carcasses to be cut down and given to some priestly attendants to burn without the camp, in conformity with the general law for the sin offerings (Lev 4:8-12; Lev 8:14-17). The persons employed in burning them, as well as the conductor of the scapegoat, were obliged to wash their clothes and bathe their flesh in water before they were allowed to return into the camp.
lev 16:29this shall be a statute for ever unto you, that in the seventh month ye shall afflict your souls--This day of annual expiation for all the sins, irreverences, and impurities of all classes in Israel during the previous year, was to be observed as a solemn fast, in which "they were to afflict their souls"; it was reckoned a sabbath, kept as a season of "holy convocation," or, assembling for religious purposes. All persons who performed any labor were subject to the penalty of death [Exo 31:14-15; Exo 35:2]. It took place on the tenth day of the seventh month, corresponding to our third of October; and this chapter, together with Lev 23:27-32, as containing special allusion to the observances of the day, was publicly read. The rehearsal of these passages appointing the solemn ceremonial was very appropriate, and the details of the successive parts of it (above all the spectacle of the public departure of the scapegoat under the care of its leader) must have produced salutary impressions both of sin and of duty that would not be soon effaced.