Versus is a basic Player vs Player mode in which 2 or more players duke it out on an arena of their choice until only one is left standing. Typically this is done by way of draining the health of other people's health to empty, but a time limit can also be imposed so that the one with the highest remaining health is declared the winner. All players fight for a specific # of rounds (typically as a best of 1, 3 or 5) until one player wins the number of rounds given and is declared the overall winner.
Like in Single Player, players can also bring multiple characters to a fight at a time, switching between them as the situation demands. Most of the victory conditions still remain the same - KO everyone else's characters, or have the highest overall health across your team out of everyone else's when the timer expires.