The shofar is blown on Rosh Hashana in order to recall our merits before G‑d on the Day of Judgment. In fact, I think it’s blown something like 100 times. But why is the shofar blown on Yom Kippur? Or more accurately, why is it blown after the “Neila” service, once the day is already over?
There are different customs about how to blow the shofar after “Neila”, the concluding prayer of Yom Kippur. According to the Ashkenazi custom, one long tekia blast is blown after the last kaddish. According to the Sefardim and Chasidim, 10 shofar sounds are blown during the kaddish, followed by the long tekia after the kaddish.
There are a number of reasons for the sounding of the shofar at the conclusion of Yom Kippur:
It is a memorial to the Jubilee year in which slaves were set free and lands were returned to their original owners; this commenced with the shofar being blown after Yom Kippur.
It is intended to confuse and confound Satan who attempts to make his final accusations upon the conclusion of the Day of Atonement.
It signals the victory over Satan’s accusations and rejoicing over our resulting atonement.
As on Rosh Hashana, it recalls the merit of the binding of Isaac at this final sealing of the Divine decree.
It recalls the atonement of the Jewish People upon Moses’s descent from Mount Sinai on Yom Kippur, which was accompanied by the blowing of the shofar.
It signifies the return of the Divine Presence to the heavenly realm, which was also accompanied by the shofar.
It formally announces the end of the fast and the onset of night, enabling the people to eat.
It lends a holiday ambiance to the meal which breaks the fast and should be conducted in a festive manner.