Rosh Hashana, the Jewish New Year, falls on the first day of the month of Tishrei. On that day, we are commanded to hear the sound of the shofar, a horn cut from a ram or other kosher animal. Our verse calls Rosh Hashana “yom teruah,” “a day of sounding the blast,” but the Torah does not spell out the obligation to use a shofar. Rather, it is learned from cross-analysis with Leviticus 25:9, where the word teruah is specifically used to refer to sounding a shofar blast.
A shofar must be curved, not straight. It comes from a male kosher animal but not from cattle. (A bull’s horn would be called a keren rather than a shofar.) The sound made by a shofar is a mournful wail. There are three styles of blasts corresponding to three different sounds of crying. In this fashion, everyone gets to hear a set of shofar blasts that sounds like crying to him.
The reason we sound the shofar is because Rosh Hashana is a time for teshuva (repentance). The shofar is meant to rouse us, to inspire us, and to turn our hearts back towards God. Additionally, the horn is symbolic of the ram that was offered by Abraham in lieu of Isaac in Genesis chapter 22. Abraham had been willing to sacrifice his beloved child to fulfill the will of God but in the end he was only required to offer a ram that had been caught in a thicket by its horns.
This mitzvah applies in all times and places; only men are obligated but women are accustomed to hear the shofar as well. In the Talmud, this mitzvah is discussed in tractate Rosh Hashana (16a-b, 26a-30a). It is codified in the Shulchan Aruch in Orach Chaim 585. This mitzvah is #170 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #30 of the 77 positive mitzvos that can be fulfilled today in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.