Your souls, i.e. yourselves, by fasting and abstinence from all delightful things, and by compunction and bitter sorrow for your sins, and the judgments of God either deserved by you, or inflicted upon you for your sins. See Leviticus 16:29,30 Leviticus 23:27.
Related Commentaries of Numbers 29:7
Numbers 29:7
7 And ye shall have on the tenth day of this seventh month an holy convocation; and ye shall afflict your souls: ye shall not do any work therein: