The Gemara in Rosh HaShanah (16a) indicates that the reason we blow the Shofar on Rosh HaShanah is that the Torah has told us to do so. Despite the many famous symbolisms and lessons associated with the Mitzvah of Tekias Shofar, the Gemara is telling us that ultimately, it is simply because the Torah has told us to sound the Shofar that we perform this act on Rosh HaShanah. Indeed, the posuk in Tehillim (81:5) recited on Rosh HaShanah as part of the "Shofaros" section of the Musaf Shemoneh Esrei, as well as during Maariv after the Birchos Kerias Shema and, according to some, as an introduction to the daytime Kiddush, can be understood as referring to Tekias Shofar as a "Chok", a Mitzvah whose rationale is not readily apparent. It has been commanded by HaShem and we are thus obligated to fulfill it.
Nonetheless, it would appear from a subsequent passage in the Gemara there that the Mitzvah of Tekias Shofar is in fact different from other Mitzvos. The Gemara states that in any year in which the Shofar is not blown at its outset, people will cry at its conclusion. Rabbi Meir Simcha HaKohen of Dvinsk, in his Meshech Chochmah (on Parshas Emor), states that failure to fulfill other (positive) Mitzvos does not result in a penalty if the omission was due to circumstances beyond one's control. According to this Gemara, however, such is not the case regarding Shofar. Rather, there is a negative result when the Shofar is not blown on Rosh HaShanah.
According to the Mesech Chochmah, Shofar is analogous to medication prescribed for one who is sick. If a sick person fails to take the correct dosage of his medication, his illness will get worse and he will not recover, even if his reason for not taking the proper medication is valid. Similarly, since the Shofar sounds are like "medication" for the soul, if one does not hear them on Rosh HaShanah, even for a valid reason, the soul will not heal. Medication is designed to fight the causes of one's physical ailment; the sounds of the Shofar fight the cause of one's spiritual ailments, namely the Yeitzer Hora. Consequently, if one does not hear the Shofar at the start of the year, the Yeitzer Hora will remain strong and the ultimate result will be crying and sadness down the road. Since the Shofar calls us to do Teshuvah, one who does not hear the Shofar is not left merely having forfeited a Mitzvah, but rather one is left without a "weapon" against the Yeitzer Hora and in favor of Teshuvah. Like the person who is physically ill and does not take his medication, such a person will have a tough time, at least in terms of his spiritual survival.
Let us all hear the Shofar sounds this Rosh HaShanah with the intent of fulfilling a Mitzvah from the Torah while at the same time focusing on the roll that the Shofar can play in assisting us on the road to Teshuvah and spiritual recovery. Best wishes for a Kisiva V'Chasima Tovah to all!!