The festival of Rosh Hashanah—the name means “Head of the Year”—is observed for two days beginning on 1 Tishrei, the first day of the Jewish year. It is the anniversary of the creation of Adam and Eve, the first man and woman, and their first actions toward the realization of mankind’s role in G-d’s world.
The central observance of Rosh Hashanah is the sounding of the shofar, the ram’s horn, which also represents the trumpet blast of a people’s coronation of their king. The cry of the shofar is also a call to repentance, for Rosh Hashanah is also the anniversary of man’s first sin and his repentance thereof, and serves as the first of the “Ten Days of Repentance” which culminate in Yom Kippur, the Day of Atonement. Another significance of the shofar is to recall the Binding of Isaac which also occurred on Rosh Hashanah, in which a ram took Isaac’s place as an offering to G-d; we evoke Abraham’s readiness to sacrifice his son, and plead that the merit of his deed should stand by us as we pray for a year of life, health and prosperity. Altogether, we listen to one hundred shofar blasts over the course of the Rosh Hashanah services.
Source: chabad.org
In 2021 Rosh Hashannah in USA falls on September 6.