Shofar is the rams horn that we sound each morning during the month of Ellul, on Rosh Hashanah (unless it falls on Shabbat) and at the close of Yom Kippur.
The word shofar comes from a root meaning rounded, which describes the shape of the shofar. (A shfoforet is a tube or egg shell.) This shape was not uncontroversial. The Talmud (Rosh Hashanah 26b) cites an argument about whether the shofar for Rosh Hashanah should preferably be bent to symbolise a bowed and contrite posture on the Day of Judgment, or straight to indicate our upwards yearning.
Related to this sense of roundedness, shafar means smooth, pleasing or cheerful, and the verb shiper means cleanse, conciliate or harmonise.
These cognate meanings allow for some creative midrashic puns. For example, in the month of Tishri, when the shofar is sounded, we are told: shapru, cleanse or harmonise our deeds (Vayikra Rabba 29).
The shofar blasts have accumulated many symbolic meanings, though none more famous than Maimonidess suggestion (Hilchot Teshuvah, 3:4) of a call to self-awareness: Wake up, sleepers get up, slumberers examine your actions, repent, and remember your Creator these are the people who forget the truth in the toils of time, and strive for years after vanity and emptiness that cannot help or save them.