Day of Atonement: Leviticus 16:1-34

“The Day of Atonement Ritual: Occasioned by the death of Nadab and Abihu (ch.10), the prescription sets out how ~ and for what purpose ~ Aaron the chief priest is to enter the Most Holy Place. The account ends with the institutionalization of the ritual (16:29-34). The nature of the ritual shows that the purification for sins and uncleanness must be done from the innermost part of the tabernacle. All other purificatory rituals hinger on the ceremony of this say. The sin offerings in this chapter in particular point to the work of Christ on the cross (see Heb.9:7-14).”  Taken from the commentary notes of the ESV Study Bible 2008 edition.

“And it shall be a statute for you forever that in the seventh month on the tenth day of the month, you shall afflict yourselves and shall do no work, either the native or the stranger who sojourns among you. For on this day shall atonement be made for you to cleanse you. You shall be clean before the LORD from all your sins. It is a Sabbath of solemn rest to you, and you shall afflict yourselves, it is a statute forever (emphasis mine)” (Leviticus 16:29-31).

Note that the word afflict is used twice. The Hebrew word for afflict is anah or awnaw. It means to weaken, humble, abase, or emaciate oneself. It does not mean fast; thus, this isn’t a command to fast per se. However, it was understood that fasting must necessarily be done to weaken and emaciate oneself. To inflict means to impose on oneself. It’s an action verb. It’s intentional. It’s more than self-denial. This is why although the term fasting is not used in Leviticus, it is associated with Yom Kippur (the Hebrew words which translate to Day of Atonement) today. Fasting is a way to inflict oneself. 
According to the Jewish oral tradition, the affliction of Yom Kippur (a 25-hour period) consists of five prohibitions, one of which is no eating or drinking (fasting). The others are no wearing of leather, no bathing or washing, no sexual relations, and no anointing oneself with perfumes, lotions, creams, or oils. In other words, it is not life as usual during Yom Kippur.