Leviticus 23:27
ESV - 27 Now on the tenth day of this seventh month is the Day of Atonement. It shall be for you a time of holy convocation, and you shall afflict yourselves and present a food offering to the Lord.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Usually, this denial of self means "fasting"--going without food and/or drink. But it also can mean abstaining from other things such as changing one's clothes, bathing or sex (2 Samuel 12: 20).
See the Quest Study Bible.