It's an optional sidequest.
FFI SPOILERS
(SPOILER) Right after you obtain the airship, fly NW and look for some islands with holes in them. One of them has Bahamut, who gives you a challenge. Go to the Citadel of Trials, due East of the islands. You can either park your airship far East and walk to it, or you can use your ship and canoe and use the river near by. Once you go through the Citadel and get the Rats Tail, give it to Bahamut andhe will change your parties classes.