Exdeath is the villain and boss of Final Fantasy V, a game that was never released in the United States. He shares many qualities with other video game bosses, especially RPG ones. He is maniacal, evil and possesses great powers. He prefers to fight mostly through his minions , and doesdn't bother to actually defeat the group of heroes who have banded together to fight him until the very end of the game, when it is too late.
The story of Exdeath's origin is rather muddled, and loses something in the translation. It all begins 1,030 years before the beginning of Final Fantasy V, when the ancients seal the power of The Void away. 30 years before the beginning of the game, Exdeath arises and is in turn sealed away by the "four warriors of dawn". When the game begins, Exdeath awakens, and tries to use the power of the void to destroy all of the worlds.
Exdeath, much like the villain of Final Fantasy VII isn't looking to control or dominate the world, as many RPG villains want to. His goal is nothing but the return of the world into a primordial soup of chaos where nothing will exist and all memories will be vanquished for eternity. As such, he represents not so much evil as a form of nilhism. A somewhat sophisticated concept for a game that is mostly spent wandering around getting into random fights to level up.
As for fighting Exdeath, which happens several times in the game, he follows the usual pattern of bosses in RPGs. He has a very very high amount of hit points, and will attack repeatedly with magic attacks, but will not actually try to finish you off with physical attacks. It is relativly easy to beat him all the times you fight him by finding the right tempo of healing your party and counter attacking with magic.