You give them to soem NPC in Jueno when you get 40, 50, or 60 (you give that amount) and then your allowed to go fight a boss, depending on the number it's level will change, also when entering the area where he's at, you'll see a level cap, so if your level 60 and the cap is 50, you'll lose 10 levels for this battle and get them back when you leave.

If you win you get lot's of good stuff worth quite a bit of money. I hear the usual drop value from one of these guys is supposed to be about 100,000 gil,