The Gemara (Rosh Hashanah 16) asks, "Why do we blow shofar with a ram's horn (איל של שופר)? Hakadosh Baruch Hu says, 'Blow for Me with a ram's shofar so that I will remember akeidas Yitzchok, and I will consider it as though you were bound on the akeidah before Me.'"
A part of a ram is used, to arouse Hashem to remember Akeidas Yitzchak. But one can still ask why specifically the horn, the shofar, is used? For example, the Torah could have given us a mitzvah to hold the ram's foot or some other limb. Why specifically the horn?
We can answer that the ram's horn reminds heaven of the struggles and the hardships the Jewish nation goes through to do Hashem's will. Chazal tell us that the ram tried to run to the Akeidah to do Hashem's will, but it got tangled in the bush, and it couldn't come out, until Avraham came and untangled it. So, we blow with the ram's horn (a) to arouse Hashem to remember the merit of Akeidas Yitzchak, (b) and particularly the horn/shofar, to arouse Hashem to remember all the struggles and hardships the Jewish people endure to perform Hashem's will.
The Gemara (Rosh Hashanah 16) says that we blow the shofar before Shemoneh Esrei (תקיעת דמיושב) and again during Shemoneh Esrei (תקיעת דמעומד) to confuse the Satan.
How does blowing the shofar twice confuse the Satan? Tosfos (quoting the Yerushalmi) explains that in the future, a great shofar will be blown, as it states, גדול בשופר יתקע ההוא ביום והיה, "On that day, a great shofar will be blown..." and then the Satan will be judged and slaughtered. When the Satan hears the first set of tekiyos, "He is afraid, but isn't completely afraid." He fears this might be the shofar heralding the future world when the Satan will be eliminated, but he isn't sure. When he hears the shofar a second time, the Satan says, "This must certainly be the shofar gadol. The time of my destruction has arrived." Confused and frightened, he can't speak kitrug, lashon hara on the Jewish people.
We wonder why the Satan is so afraid. Doesn't he remember from last year and from years before that we blew the shofar on Rosh Hashanah? Why does he suspect that this year may be different?
The Satmar Rebbe zy'a answers that in each generation, the tests become harder. Every year, it becomes harder to serve Hashem. The Satan thinks, "This year, due to all the challenges and hardship, the Jewish people are far more precious than ever." Therefore, he fears that the shofar he hears is the shofar gadol of Moshiach."
