In the third chapter of Hilchot Teshuva (Halacha 4; listen to audio for precise citation), the Rambam (Rabbi Moshe Maimonides, Spain-Egypt, 1135-1204) discusses the symbolic meaning of the Misva of Shofar. He writes that although the sounding of the Shofar is a "Gezerat Ha'katuv," a Biblical command like any other, which we perform for its own sake regardless of any reason or rationale to which we could attribute it, this ritual also serves an important symbolic function. The sounding of the Shofar is intended as a kind of "alarm clock" to "awaken" us from our spiritual "slumber," from our preoccupation with the vanities of the world. People have a tendency to focus their minds upon the pursuit of physical pleasures and material acquisitions, rather than upon "Avodat Hashem" – the service of God. The sounding of the Shofar is thus intended to "awaken" us from this mindset and remind us to make Torah and Misvot our highest priority.
One Rabbi remarked that the manner in which the Shofar is held reinforces this symbolism. The Ba'al Toke’a (person sounding the Shofar) holds the Shofar with the wide end facing upwards, while the narrow end is held lower. This positioning symbolizes the fact that we should look towards the "ground," our mundane pursuits, with the "narrow end," as matters of secondary importance. The heavens, by contrast, should be given the "wide end," our highest priority and central focus. The Shofar bids us to refocus our attention upon Torah and Misvot, and to relegate our physical and material pursuits to secondary status.
In this context the Rambam mentions the widespread practice among all Jewish communities to increase charitable donations, prayers and performance of Misvot during the period from Rosh Hashanah to Yom Kippur. In particular, we arise in the early morning hours to recite special Selihot prayers to beseech God for forgiveness. As this is the period when we are judged for the coming year, we double our efforts in performing Misvot and add special prayers in the hope of securing a favorable judgment for a successful year of blessings and good health.