The Gemara asks why the shofar is blown twice: first, after the Torah reading and then a second time, divided into three sets, during Mussaf. The Gemara then answers, “to confound the Satan.”
The Ran explains that here the Satan refers to Yetzer Hara, and “to confound the Satan” means to subdue or vanquish the Yetzer Hara.
The Tur presents two ways to understand the dynamics at work here: 1) To confound the Satan right away during the initial set of shofar blasts so that it is incapable of lodging claims during Mussaf. 2) To overwhelm the Satan during the initial shofar blowing, leaving the Satan reeling during the latter shofar blasts.
The Talmud Yerushalmi cites two verses: “He will swallow up death for ever…” (Yeshayahu 25:8) and “And it shall come to pass in that day, that a great horn shall be blown; and they shall come that were lost in the land of Assyria, and they that were dispersed in the land of Egypt; and they shall worship the LORD in the holy mountain at Jerusalem” (Yeshayahu 27:13).
The Gemara then proceeds to present the following interpretation: “When [the Satan/Yetzer Hara] hears the first sounding of the shofar it is startled, but unfazed, saying, ‘Perhaps the time for the Great Shofar has arrived.’ [But] when [it] hears the second time it says, ‘Certainly the time has arrived’ and it becomes confounded and is no longer free to serve as Prosecutor.”
The Smag explains that the Satan will not conclude that the time for the Great Shofar has arrived. However, it does serve as a reminder that when the time comes the Great Shofar will decimate him, therefore it is akin to a person who sees a dead person and therefore starts to contemplate his own end.