The center of the floor? If it was a drop from one side of the room to the other I'd say it has to do with the house settling unevenly. But if it's in the center of the room it seems the joists have been under a lot of strain at some time, like something really heavy in the middle of the room, maybe a water bed. Also, if it leaked the joists would have gotten wet, allowing them to flex even more.
It seems to me the joists are bowed, in which case you may have to take up the floor and sister straight joists to the existing ones - not a small task for the average do it yourselfer.
This is just off the top of my head. You'll get replies from others pretty soon, who might have some better ideas.