The unique element of the Rosh HaShana prayers are the three special blessings added to the additional prayer [Musaf]: Kingships, Remembrances, and Shofarot.

Recite before Me on Rosh HaShana the blessings of Kingships, Remembrances, and Shofarot: Kingships so that you will crown Me as King over you; Remembrances so that your remembrance will ascend before Me for good; and with what? With the shofar.

Rabbi Abbahu said: Why does one sound the shofar with a ram’s horn? The Holy One, blessed be He, said: Sound the shofar before Me with a ram’s horn, so that I will remember for you the binding of Isaac son of Abraham, and I will ascribe it to you as though you have bound yourselves before Me. (Rosh HaShana 16a)