The Final Summoning in Final Fantasy X is the calling of the Final Aeon that the Summoner performs at the end of their Pilgrimage. The Final Summoning is the only means of destroying Sin and granting the Calm to the people of Spira.
Yuna and the others learn that the Final Summoning is nothing more than the sacrifice of person that is dear to the summoner to prolong the cycle of the false truths. The summoner dies after calling the Final Aeon, presumably being killed by it.
Refusing to repeat the endless cycle, the party defeats Yunalesca, and decides to destroy Sin once and for all, without the use of the Final Summoning.
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