A double K.O. occurs when both players perform a knockout on each other at the same time. It generally occurs because both players run low on life, then trade hits (often in the hopes that the opponent wouldn’t try as well).
If the game was between the player and the computer, the player usually loses.
When the matter comes to rounds, some games will award the round to both players; from there, some games will give the match to the player who was ahead, while other games will give a round to the player who is behind, leading to the third or perhaps “final” round. Some games, in the event of a tie where no rounds can be awarded, will either make a judgment, or go into some sort of overtime (maybe an extra round, maybe a “sudden death” setup).
When the matter comes to teammates, the game is more likely to make a judgment when the last two characters go down if the game is about tag teams; otherwise, the matter is determined with additional rounds between the last members (maybe).
All of these mechanisms really do depend on the game, though some developers have noted preferences for one system over the other.