Important stuff:
There was this Big Bad monster that kept blowing up cities. So people called 'summoners' went to fight them, but the ended up sacrificing themselves only to reincarnate the Big Bad ten years later. This turned into a ritual for the world. If you die and are not 'sent' by a summoner, you more or less become a pms-ing zombie.
Yuna was a summoner, beat up Sin without dying, met this guy kinda created by the 'Gods' called fayth, and in the meantime killed the bad guy name Seymour.
As a kid, Seymour and his human mother were exiled to an island (strangely full of man-eating lizards), while his Guado (a race that watches over the gateway to the afterlife world called the farplane) father dealt with a civil war. Two years later, Seymour's mother commits suicide and becomes a Fayth to live in the happy afterlife. For some reason she blames Seymour for him feeling everyone will be happier dead than alive and not herself.
Seymour grows up, plans to become a summoner but doesn't, and eventually kills his father, inheriting his father's position as leader.
There is also another race called the Al Behd who make machines, which are forbidden to all other races. They're supposed to e good guy underdogs.
Need any more explanation?