“On the tenth day of this seventh month.” This is the Day of Atonement (Lev. 16; 23:26-32).
“you are to afflict your souls.” In the context of the Day of Atonement, which was the tenth day of the seventh month (Nisan calendar) the primary meaning of the phrase “afflict your souls” is to go without food, to fast (see commentary on Lev. 16:29).