The Rat tail is an important item that Bahamut orders the Light Warriors to find, so he may make himself some soup. Upon finding out what the soup is for, the Light Warriors find out that maybe it's best to not ask questions.
Bahamut orders the Light Warriors to find him a Rat Tail, a Dire Rat Tail, so that he can make some soup. When the Light Warriors find out the purpose of this soup, they are less than thrilled, mostly because it is essentially a cure for Bahamut's impotence.
Dragoon tries ordering some of the same soup at a restaurant during the epilogue but Red Mage quickly overrides him and tells him to get Nachos instead.