It's fairly simple once it all comes together.
I might have some details wrong though, as this is from memory:
- 1000 years ago, Zanarkand vs Bevelle
- Zanarkand has lots of summoners e.g. Yu Yevon and his daughter Yunalesca.
- Yu Yevon gathered the remaining citizens of Zanarkand who were losing the war against Bevelle and made them Fayth (who dreamnt of the old Zanarkand) and created Sin as an armour.
- If a summoner sacrifices one of their close guardians for use as a Fayth, they become an even stronger Aeon known as the Final Aeon which will kill both Sin and the summoner allowing Yu Yevon to manipulate it and use it form the new Sin as armour to protect himself.
- Jecht is a dreamt of the faith, is taken into the real Spira, meets Braska and Auron, becomes Braskas final Aeon, defeats Sin/kills Brasksa and becomes the new Sin after the period of the calming.
- Auron is ******, goes for revenge against Yunalesca who helped them make the final aeon, is killed but doesn't go to the farplane.
- Auron travels into the Fayth's dreams, watches over Tidus as he promised Jecht and eventually Sin (with Jecht's soul) is drawn into the Fayth's world to see his son, and ports both Auron and Tidus into the real Spira.
- Tidus' Quest ensues, lots of other key plot points here, but I want to keep this short
- Yuna rejects the idea of a Final Aeon that all summoners before her chose, kills Yunalesca and along with her friends manages to defeat Sin's external shell and as she's not dead (having no final Aeon to kill her) she travels inside Sin and fights Braska's Final Aeon (i.e. Jecht) who is being manipulated by Yu Yevon as all other Final Aeons were to power the armour/shell of Sin.
- Jecht/Braska's final Aeon is killed
- Yu Yevon comes out to fight, he dies
- Auron goes back to the farplane, at peace.
- Tidus was a dream created by the Fayth, thus now that they are not controlled by Yu Yevon, they can finally stop dreaming and as such Tidus as a creation of their dream, dissapears (he only reappears in the good ending of FFX-2 as the Fayth want to say thanks for Yuna saving the world from Vegnagun and thus they dream him up again so he can live his life with Yuna).