The first place that atonement is mentioned directly, by name, is in the book of Exodus. Scripture states, "And they (Aaron the High Priest and his sons) shall eat those things with which the atonement was made to consecrate and to sanctify them . . . (Exodus 29;33, HBFV)
The tenth day of the seventh month (named Tishri) in the Hebrew calendar is the Day of Atonement. It was a time when an annual ritual was performed to take away the sins of the people (Leviticus 23, Hebrews 9:22). Today, during this twenty-four hour period, true Christians do not eat anything at all and come together to worship of Lord.
Aaron (the brother of Moses), in the symbolism of Atonement, represents Christ (Leviticus 16:4 - 6. The Most Holy Place, also known as the 'Holy of Holies," represents God's throne in heaven. Since Aaron, as a human being, is of himself unqualified to stand before God he must be ceremonially cleansed and have his sins forgiven.
One of the most unique events in the Old Testament occurs on this special day. Aaron (and those High Priests which came after him) were commanded to randomly select (via lots) one goat to represent "the Lord" and another one to represent "Azazel" (Satan the devil, the being chiefly responsible for our sins). Casting lots is an ancient way of allowing God to decide something rather than imperfect man (Leviticus 16:8, 10, 26).
The centerpiece of the Day of Atonement begins when the Azazel goat has the sins of the people placed on it by Aaron. It was then released into the wilderness. The goat that represented Jesus Christ was killed as a sin offering. The blood from the sacrifice was then taken by the High Priest into the tabernacle's (later, the temple's) Holy of Holies.
The High Priest was allowed, only once a year during Atonement, to enter the most holy section of the entire tabernacle (temple). Once in the Holy of Holies, the priest sprinkled the blood from the sacrifice on the mercy seat of the Ark of the Covenant. This represented Christ, on the Sunday after his resurrection, presenting his blood as a sacrifice for all sin to God in heaven.
The primary reason true Christians fast on Yom Kippur is that it is commanded by God. The day focuses the mind on what the Eternal is doing and reminds believers about his great mercy and compassion for ALL people. On the day of Atonement believers fast for a full 24 hour period. In 2017, this special day occurs on September 30 (it begins the previous evening for all dates). In 2018 it occurs on September 19, in 2019 it occurs on October 9, and in 2020 it occurs on September 28.