The Shofar is a ram’s horn, which is blown throughout the month of Elul and on Rosh HaShanah. Its sound is meant to arouse us to do Teshuvah.
The Shofar also serves as a reminder of the ram which was “caught by its horns in the bush.” (Bereshit {Genesis} 22, 12)
As the Torah recounts, G-d brought this ram to Avraham, who was at the time demonstrating his willingness to sacrifice his son, Yitzchak, as G-d had commanded him. At the last moment, G-d made this ram appear, “caught by its horns in the bush, ” and told Avraham to sacrifice the ram rather than his son Yitzchak – thus teaching Avraham the concept of Divine mercy.
The Shofar is an eternal symbol, which we ask G-d to “remember” in our behalf, for the act of Avraham, known as Akeidat Yitzchak (the “binding” of Yitzchak, as if for a sacrifice) represented the greatest height to which a human being can rise.
With the blowing of the Shofar we ask that just as Avraham suppressed his natural feelings of mercy towards his son, G-d suppress His attribute of Strict Justice which would require the inflicting of deserved punishment upon us.
The Shofar also represents “majesty.” It was blown when G-d gave the Torah to the Jewish People at Mount Sinai, and will be sounded again upon the arrival of the Mashiach.