Yom Kippur, also known as the Day of Atonement, is the most important holiday in Judaism, centering around the themes of atonement and repentance. Its origins can be found in Leviticus 16:29-34:
“This shall be a statute forever for you: In the seventh month, on the tenth day of the month, you shall afflict your souls, and do no work at all, whether a native of your own country or a stranger who dwells among you. For on that day the priest shall make atonement for you, to cleanse you, that you may be clean from all your sins before the LORD. It is a sabbath of solemn rest for you, and you shall afflict your souls. It is a statute forever. And the priest, who is anointed and consecrated to minister as priest in his father’s place, shall make atonement, and put on the linen clothes, the holy garments; 33 then he shall make atonement for the Holy Sanctuary, and he shall make atonement for the tabernacle of meeting and for the altar, and he shall make atonement for the priests and for all the people of the assembly. This shall be an everlasting statute for you, to make atonement for the children of Israel, for all their sins, once a year.” And he did as the LORD commanded Moses.
As can be seen in the passage from Leviticus, Yom Kippur originally featured a sacrificial component. After the destruction of the temple, sacrifices could no longer be offered, and so a recitation of the sacrificial services performed in the temple was included in Yom Kippur services. This is, according to rabbinic teaching, thought to help achieve atonement despite the inability to actually perform the required sacrificial rituals.
In modern times, Yom Kippur is usually observed by fasting for a 25-hour period and devoting large amounts of time to prayer. During the Days of Awe, which lead up to Yom Kippur, an individual searches his or her soul, repents of wrongdoing, attempts to amend his or her behavior, and seeks forgiveness for sins against the Lord and also against fellow humans.