From Wikipedia:
An ominscent being known as the Eternal Champion predicts that mankind will soon fade to existence due to the untimely and unjust deaths of key individuals throughout history who were destined for greatness. Seeking to restore balance to the world, the Eternal Champion gathers these souls from time moments before their deaths to participate in a fighting tournament. The victor will be able to change their fate and bring balance to the universe, whilst the losers will be forced to live out their deaths just as history intended.
Unlike most fighting games, or video games in general, there are no characters in this game that are "bad" or "evil". Each character has been chosen because they are either inherently good, or they have the potential to do great good and change the course of history for the better. Despite the ability to kill opponents in this game, this is not relevant to the story. Much like games such as Mortal Kombat (which pioneered finishing moves in fighting games), the game's "Overkills" are not canon and simply a gameplay element for the enjoyment of the player. It is actually revealed in a few character endings that some of the fighters had become allies or friends during the course of the tournament.