The breaking wave a surfer rides is called a transition wave. This differs from the original swell formed out at sea.
The swells made by the wind are vasically an up and down motion of the water molecules, and the only forward motion is a wave motion. As soon as the swell reaches water about one-and-a-half times as deep as its size it begins to break,
and the forward motion changes from a wave motion to an actual forward motion of the water. As the water gets shallower, the swell is pushed upwards.
This colllum of water becomes unstable, and because the wave is contiually slowing down as it moves into shallower and shallower water, the forward momentum causes the lip to fall over forwards. this is what causes the distinctive shape of a breaking wave.
The intensity of the wave is determined by the slope of the bottom. A steep bottom means that the wave is coming out of deep water and therefore traveling fast.
Because the bottom gets shallow quickly the wave peaks up and slows down dramatically which makes the lip throw far and thick.
Although this makes a wave difficult to paddle into becuase of the quick trasition from swell to barrel, good surfers are able to make use of the far-throwing lip to pull into some wide, wide barrels.