Rosh Hashanah is the start of the civil year in the Hebrew calendar (one of four "new year" observances that define various legal "years" for different purposes as explained in the Mishnah and Talmud). It is the new year for people, animals, and legal contracts. The Mishnah also sets this day aside as the new year for calculating calendar years and sabbatical (shmita) and jubilee (yovel) years. Jews believe Rosh Hashanah represents either analogically or literally the creation of the World, or Universe. However, according to one view in the Talmud, that of R. Eleazar, Rosh Hashanah commemorates the creation of man, which entails that five days earlier, the 25 of Elul, was the first day of creation of the Universe.
Yom Kippur
Yom Kippur is the tenth day of the month of Tishrei. According to Jewish tradition, God inscribes each person's fate for the coming year into a "book" 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 considers one's self absolved by God.
Yom Kippur