Yom Kippur is the holiest day of the year—the day on which jews are closest to G-d and to the quintessence of their own souls. It is the Day of Atonement—“For on this day He will forgive you, to purify you, that you be cleansed from all your sins before G-d” (Leviticus 16:30).
For nearly twenty-six hours—from several minutes before sunset on 9 Tishrei to after nightfall on 10 Tishrei—jews “afflict their souls”: they abstain from food and drink, do not wash or anoint their bodies, do not wear leather footwear, and abstain from marital relations.
The day is the most solemn of the year, yet an undertone of joy suffuses it: a joy that revels in the spirituality of the day and expresses the confidence that G-d will accept repentance, forgive sins, and seal the verdict for a year of life, health and happiness. The closing Neilah service climaxes in the resounding cries of “Hear O Israel . . . G-d is one.” Then joy erupts in song and dance (a Chabad custom is to sing the lively “Napoleon’s March”), followed by a single blast of the shofar, followed by the proclamation, “Next year in Jerusalem.” People then partake of a festive after-fast meal, making the evening after Yom Kippur a yom tov (festival) in its own right.
Source: chabad.org
In 2020 Yom Kippur in USA falls on September 28.