Wakeboards aren't just objects that float on the top of the water, moving you haphazardly wherever you steer them with your feet. They have components called fins, which are affixed to the underside of the board and act as a pair of (usually plastic) "claws" that grip -- or at least inhibit the flow of -- water as the board travels. Fins are a lot like a boat's rudder in that their placement keeps the board moving in a controlled, forward manner, which is the way you want it to move. Without the fins, the wakeboard would be much more likely to wildly and freely rotate on the water's surface, which would make riding the board, let alone attempting tricks, extremely difficult.
There are all sorts of specialized fins available, but in general, they come in two types: wide and thin. While both serve the same general purpose, a wide fin is better suited to beginners and intermediate wakeboarders. It moves more water around the board to create drag, which offers some additional stability. But even experienced wakeboarders opt for a wide fin sometimes -- in choppy water, for example, they're good insurance. Otherwise, the more advanced or adventurous wakeboarder may go for a thin fin [source: Discover Boating]. The thin fin pushes less water, and thus offers less drag. This might mean that the board will rotate on the water a bit more, but it also means the advanced rider will have more user-generated control and freedom to perform stunts.
You now know how the various elements of the board function, so there's just one more thing to consider -- the board itself. Keep reading to find out how size comes into play.