The blowing of the shofar has many purposes and many layers of meaning.
The blowing of the shofar, which is typically made of a ram’s horn, calls to mind the ram that the Patriarch Abraham sacrificed instead of Isaac. And it helps us remember to feel fear of Hashem’s glory, as it says in Amos 3:6: “If a ram’s horn is sounded in the city, can the inhabitants fail to be alarmed?”
R’ Mordechai Housman writes that the word “shofar” is similar to the word shapru, Hebrew for “beautify,” which is to remind us to “beautify” our deeds and correct our actions. The shape of the shofar is very indicative of our relationship with Hashem.
The shofar has one narrow end and one wide end. We blow into the shofar at the narrow, tapered end, and the sound comes out of the wide end, as in some musical instruments. On Rosh Hashana, the verse “From the straits I called upon Hashem, Hashem answered me expansively” (Psalms 118:5) is recited before the Blowing of the Shofar. In other words, when we are in dire straits, in a bind, we pray to G-d for help and support.
According to Leo Rosten, “The bend in the shofar is supposed to represent how a human heart, in true repentance, bends before the Lord. The ram’s horn serves to remind the pious how Abraham, offering his son Isaac in sacrifice, was reprieved when God decided that Abraham could sacrifice a ram instead.”