Jamieson, Fausset and Brown on Leviticus 16:29-34

29-34. this 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 [Ex 31:14, 15; 35:2]. It took place on the tenth day of the seventh month, corresponding to our third of October; and this chapter, together with Le 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.