Square-Enix draws inspiration from the mythology of many cultures for the summoned creatures in its Final Fantasy series of games. Bahamut is no exception. In the Arabic legend, Bahamut is a very large fish. It is so large, in fact, that a bull, Kujuta, stands on its back. Atop that bull is a ruby mountain. Above the ruby mountain there is an angel, six hells, the Earth, and finally seven heavens.
I told you Bahamut was big. How Square made the jump from giant fish to giant dragon, I'm unsure, but they take liberty with many of their summons. Shiva comes to mind — traditionally, she is known as "Shiva the Destroyer," but Square would have us believe that she is some sort of ice goddess. It seems almost as though Square is just looking for cool-sounding names for their summons.
Bahamut is traditionally one of the most powerful summons in any Final Fantasy game in which he appears, and he appears in the following Final Fantasy games: