From the Rosh Hashanah Wikipedia Page:
Rosh Hashanah (Hebrew: רֹאשׁ הַשָּׁנָה, literally "head of the year") is the Jewish New Year. The biblical name for this holiday is Yom Teruah (Hebrew: יוֹם תְּרוּעָה), literally "day [of] shouting/blasting", sometimes translated as the Feast of Trumpets. It is the first of the High Holy Days (Hebrew: יָמִים נוֹרָאִים Yamim Nora'im, lit. "Days of Awe") specified by Leviticus 23:23-32, which usually occur in the early autumn of the Northern Hemisphere.
Rosh Hashanah is a two-day celebration, which begins on the first day of Tishrei. Tishrei is the first month of the Jewish civil year, but the seventh month of the ecclesiastical year.
Rosh Hashanah has its origin in the beginning of the economic year in the ancient Near East, marking the start of the agricultural cycle. In its theological interpretation, the day is said to be the anniversary of the creation of Adam and Eve, the first man and woman, and their first actions toward the believed realization of humanity's role in God's world.
Rosh Hashanah customs include sounding the shofar (a hollowed-out ram's horn), following the prescription of the Hebrew Bible to "raise a noise" on Yom Teruah; and eating symbolic foods such as apples dipped in honey to evoke a "sweet new year".