What happens is that when the crowd is close to synchrony, a few people, by random chance, may start clapping together. They're not doing it deliberately, and in isolation, their brief affair may last only a few beats. But that is long enough. Because they happen to be clumped together, they are temporarily louder than anyone else within earshot, and so they are more likely to drag someone else into synchrony with them than to be dragged apart. Hence, others are likely to join them, thus boosting their signal further and dragging in others still. within seconds, they have become the nucleus around which the entire crowd has organized. But if an outside observer were to ask the ringleaders how they did it, in all likelihood they would be as surprised as anyone to discover their special status. Furthermore, if our observer were to rerun the experiment with exactly the same people in the same stadium, they would see the crowd coordinate around a different and equally arbitrary nucleus.
Much the same thing can be true of more complicated social processes, like revolutions.