Yom means "day" in Hebrew and Kippur comes from a root that means "to atone", which is related to the biblical name of the covering of the Ark (called the kapporet). Yom Kippur is usually expressed in English as "Day of Atonement".
Rosh Hashanah and Yom Kippur
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.
Heavenly books opened
According to Jewish tradition, God inscribes each person's fate for the coming year into a book, the Book of Life, on Rosh Hashanah, and waits until Yom Kippur to "seal" the verdict. During the Days of Awe, a Jew tries to amend his or her behavior and seek forgiveness for wrongs done against God (bein adam leMakom) and against other human beings (bein adam lechavero). The evening and day of Yom Kippur are set aside for public and private petitions and confessions of guilt (Vidui). At the end of Yom Kippur, one hopes that they have been forgiven by God.