The Jewish calendar is based on the cycle of the moon, which grows into a full moon and then disappears about every 30 days. The Jewish New Year begins with the transition from the Hebrew month named Elul to the Hebrew month of Tishrei (typically sometime in September or early October).
In Jewish tradition, people gather during Elul in the predawn darkness to sing Selichot (Hebrew for “forgiveness”).
Then Rosh Hashanah begins on the first of Tishrei, when the small crescent of the new moon appears in the evening sky.
The Jewish new year is called Rosh Hashanah – rosh is “head” and hashanah is “the year.” In Hebrew the word for “year” (shanah) comes from a root meaning “to change.”
How the Jewish calendar works via 18Doors