I already mentioned this in the tournament thread in the general section.
But it is basically who has dealt the most damage, done the most hits.
Which is why a lot of people are playing very campy and spamming a lot. Yesterday my partner had a match were he got up 170% in his first stock, ko'ed the other player at 70%. On the second stock he had 0% while the other player had around 50% and he lost. Because the other player, who was a Toon Link spamming arrows, got more hits in/dealt more damage.
So the problem is, that this system totally encourages a defensive spamming style. And completely punishes characters that have a hard time dealing with them, or worse, heavy characters that survive long.
It's no wonder you see so many Links and Toon Links in tournament mode.