The first Yom Kippur took place after Moses returned from Mt. Sinai a second time with the replacement set of tablets containing The Law. He had broken the first set when he returned the first time to discover the children of Israel worshipping a golden calf, rather than The Creator, who brought them out of the land of Egypt/Mizraim.
Moses pleaded with The Creator on the behalf of the children of Israel. When Moses was absence for the second time to replace the set of tablets, the nation fasted from sunrise to sunset. Upon returning, Moses found the nation truly repentant and announced that YHWH had forgiven them. He decreed that the tenth day of seventh month would remain a day of atonement for all generations. Exo. 32:1-33
Deuteronomy 9:9 and 18 show the example Moses left. He says that during his fasts, "I neither did eat bread nor drink water."
Queen Esther asked all the Israelites in Shushan to join her in a three day fast,"...neither EAT NOR DRINK three days, night or day." Esther 4:16
Ezra "...did eat no bread, nor drink water." Ezra 10:6
We find that Paul, in the book of Acts, fasted for three days, neither eating nor drinking.
Why Do We Keep The Day of Atonement?/The First Yom Kipper
After the sin of the golden calf, the Israelites wandered the desert, with the understanding that actions taken every Yom Kippur helped ensure their atonement for their sins. Leviticus 16:29-31
On this day you are to fast by refraining from eating and drinking (even water). This restriction can be lifted on this day if it is a threat to one's life or health. People with other conditions such as illnesses should either consult their physicians or Moreh. This would consist of a 24 hour fast beginning before sunset on the evening before Yom Kippur and ending at sunset on the day of Yom Kippur.
The Day of Atonement
The day of Atonement/Yom Kippur is the most important day to the Israelites. Yom Kippur means "Day of Atonement" which just means a day to set aside to "afflict the soul." On this day it is commanded to be kept on the tenth day of the seventh month, which is ten days after Yom Teruah. Only the high priest was to conduct the service on the Day of Atonement, only he could enter the Most Holy Place behind the veil to stand before The Creator. Having made a sacrifice for himself and for the people, he then brought the blood into the Holy of Holies and sprinkled it seven times on the mercy seat, the throne of The Creator Leviticus 16:14-15. Two goats are brought before the High Priest, one is sacrificed, and the other is released into the wilderness Lev. 16:20, as the sins of Israel are atoned for. The goat bears the sins of Israel into the wilderness as the high priest lays his hands on the goat confessing the sins of Israel, this act of the goat would only be kept when we return back to the land that was promised to Abraham, Isaac and Jacob, but until then it is kept today by doing no work, atoning for your sins, fasting and attending a holy convocation Leviticus 16:29-30; Leviticus 23:26-32; Numbers 29:7-11.
Israelites FASTED to afflict, humble, and chastise themselves before YHWH.
Reflect on your own need to repent. What do you need to change in your thinking about your own sin?