Yom Kippur takes place on the 10th of Tishri in the Jewish calendar. It is the day every Jew individually and collectively cleanses himself of his sins through repentance, asking for forgiveness from those he has offended before asking for it from God.
In reality, Kippur allows every human being to atone for sins committed against God, but not for those committed against other human beings unless they ask them directly for forgiveness.
For Jews, the day of Kippur is a day of atonement, a day of total fasting (25 hours), recollection and prayer in which any kind of material activity is forbidden.
The celebration of Kippur is based on Leviticus in the Torah:
"Here is a perpetual law: in the seventh month, on the 10th day, you shall humble your souls, you shall do no work,...for on that day we will make atonement for you, to purify you."
The fast ends with the sounding of the Shofar, which is meant to awaken the conscience and call for self-evaluation. It is the appropriate time for a Jew to decide to become a better person.
The day of Kippur is so important to Jews that the Marranos continued to fast in secret even during the Inquisition. As well as a duty, the day of Kippur is also a right: the right to compassion and righteousness.