summoners

Summoners are the light of Spira, bringing the Calm to the peoples. They travel to Spira's temples and pray at the Chamber of the Fayth on their way to Zanarkand, where they will get the Final Aeon and defeat Sin.

DUTIES
There are many summoners on their pilgrimage at the same time, but only one will defeat Sin. That is their primary duty, but summoners are the only ones who can perform the Ikai Okuri/Sending, a dance which sends the spirits of the dead to the Farplane.

GUARDIANS
Guardians are just that to the summoners: guardians. Although the summoner can fight with aeons, guardians ensure his/her safety along the pilgrimage. Yuna says she has as many guardians as there are friends she can trust her life with. Usually a summoner has one or two guardians.
PS. One of the guardians will sacrifice himself to become the summoner's Final Summoning, so they do that, too.

PILGRIMAGE
The summoner's pilgrimage doesn't have a straight map, but he must pray at the temples of Spira, which reside in Besaid, Kilika, Djose, Macalania and Bevelle. Each temple has it's own Fayth, which merges with the summoner and becomes and Aeon. On top of that, there are three 'hidden' temples along the way.
Summoners face many dangers during their travel, and towards the end of the journey, in Mt. Gagazet and Zanarkand, Yunalesca has sent many of these dangers to test the summoner's skill.

AEONS
Aeons are basically souls of people from 1000 years past, who died willingly and whose souls are trapped within statues of these aeons. Aeons and Fayth are one and the same, fayth remains in the Chamber and becomes and Aeons once merged with the summoner.

FINAL SUMMONING
The Final Summoning is the summon, which kills Sin. Yunalesca turns the chosen guardian into a fayth and thus into an aeon. The Summoner summons the aeon in the fight against Sin, and the final aeon rips through Sin's armour and kills it.

SIN
Sin is the armour of Yu Yevon, which is the ultimate Sin. When the Final Summoning destroys Sin, Yu's shield, it merges with with the aeon. The next few years, which are spent joicing in the Calm, Yu Yevon is gathering his power and after about 10 years, comes back with a new Sin born from the Final Summoning. Because Jecht was Braska's Final Aeon, he killed Sin, merged with Yu Yevon, and became the next Sin. And thus the spiral starts again.

KIDNAP
This is where the Al Bhed come in. The Al Bhed think there is a way to defeat Sin without the Final Summoning. They kidnap summoners and bring them to the 'Summoner's Sanctum' at Home, so they would be safe and realize killing yourself isn't worth it, because Sin always comes back.

Whew, that was long (although it doesn't look like it...)! But I hope it gives some clarity to FFX, as it's a really confusing world to those who don't know it well.