From the Yom Kippur Wikipedia page:
Yom Kippur, also known as the Day of Atonement, is the holiest day of the year in Judaism. Its central themes are atonement and repentance. Jewish people traditionally observe this holy day with an approximate 25-hour period of fasting and intensive prayer, often spending most of the day in synagogue services.
Yom Kippur is "the tenth day of [the] seventh month" (Tishrei) and is regarded as the "Sabbath of Sabbaths". Rosh Hashanah (referred to in the Torah as Yom Teruah) is the first day of that month according to the Hebrew calendar. On this day forgiveness of sins is also asked of God.
Yom Kippur completes the annual period known in Judaism as the High Holy Days or Yamim Nora'im ("Days of Awe") that commences with Rosh Hashanah.