Ok imagine you have 16 surfers in a competition.
You have 2 surfers per heat = 8 heats.
The loser of each heat is out of the competition, and the winner goes on to the next round.
So now there are 8 surfers left in the comp.
Next round (quarter finals) consists of 4 heats of 2 surfers in each heat.
Winner goes thru to next round, losers out of comp.
Next round (simi-finals) = 2 heats of 2.
Final = 1 heat of 2.
Winner of final is the champion!
In the ASP WCT and WQS events the surfers are judged on their best 2 waves of the heat. Each wave is scored out of 10 points - e.g. the perfect ride on any 1 wave would score 10 points. These 2 wave scores are added together and therefore out of a maximum of 20 points.
Incidently I think the ASP change from being judged on 3 waves/heat to 2 waves/heat is deffo loads beter. It means that the surfers are able to concentrate on getting quality rides and not just quantity, and it promotes more exciting and progressive surfing therefore.