Basically I sit between the two players, give them a certain amount of time on pre-game setup (making sure both abide by the time limit), make sure and enforce timeouts if pausing the game, and making judgment calls on any hardware malfunctions. I also have to enforce the tournament rules such as a cursing ban (since there are smaller kids that hang out at these things), settling people down if they're getting riled up, stopping any player interference between the players themselves or the spectators, and making sure they respect the hardware (no throwing, bashing or stealing).
Yeah, I didn't think it entailed much either when I signed on, but some people take this game way too seriously. I had to boot out two players and three spectators during the weekend.