With the S-shaped motion, the edge of your hand splits the water flowing past it into two streams, much like what happens when an airplane wing cuts through the air. Some water goes over the back of your hand and some goes under it. This split generates a lift, which propels you forward in the water, similar to the way a propeller's wing-shaped blades push a boat forward.

We tend to think of lift in terms of moving you upward (as is the case with an airplane), but lift can be generated in any direction, depending on the orientation of the hand (or wing) that creates it. Expert swimmers continuously adjust the angle of their hands throughout the stroke to maximize the forward-directed lift. This lift means a swimmer can go faster with less effort using the S-shaped stroke. You can almost "fly" through the water.