There are several groups of sphere hunters in Spira.
You create one character and play for one group.
The quests that each groups do varies.
Your character do a massive amounts of sidequests and such to obtain spheres and interact with NPC like Yuna, Rikku, Tidus....etc to become powerful, famous...etc.
You are to assemble a set of spheres together as the main quest which unreveal the main story of the game.
In the end, you can fight the villian after you manage to assemble the set of spheres.

BTW, why is it in the writer's corner?