I think some other people have mentioned it, but to put a little bit more detail into where the main characters are from:

In the opening cinematic, they show the adventurers fighting a massive war where Bahamut eventually gets summoned and starts laying waste to everything. They attempt to seal him away, but he breaks free in the process.

In so doing, it produces a brilliantly bright light: The Calamity. This light, apparently makes everyone everywhere forget what happened.

So presumably, these adventurers are you, the player. As powerful and awesome as ever, except you don't know it, nor does ANYONE remember what happened! So this leaves a ton of room for your own backstory, or a new one, since you could be some new guy!

There's an extended version of this intro cutscene if you sit at the title screen for a minute or so. I do really like this story, since it gives you every reason to be a massive collection of powerful warriors against some unknown massive power.