“It is a Sabbath of complete rest.” The Hebrew is shabbath shabbathon, more literally, “a Sabbath of Sabbath observance.” As any regular Sabbath, the affliction of the Day of Atonement was to last from sunset one day to sunset the next (cp. Lev. 23:32). [For more information on shabbath shabbathon, see commentary on Leviticus 25:4].
“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).