The Shofar is a kosher animal horn with the pith removed. When it is blown into its narrowest part, following a specific sequence, the mitzvah of hearing the Shofar on Rosh Hashanah is fulfilled.
The Torah calls Rosh Hashanah "The Day of the Shofar." The shofar is sounded during the two days of the holiday, unless one of those days falls on Shabbat. This year, the shofar will be sounded on September 29 and 30.
The Mitzvah itself has no reason for being, but, in any case, it indicates a kind of call to awaken from spiritual slumber and reconnect with the Source of Life, a call to recommit to our Divine mission in this world.
The Shofar is sounded after the Torah reading. Two blessings are recited beforehand, and 30 blasts are sounded. There are three types of blasts: Tekiah (one long, uninterrupted blast), Shevarim (three medium-length blasts with breaks), and Teruah (a minimum of nine short, broken blasts).