Easily explained in my opinion:
All the boards are connected in a line with a rope of some kind, creating one long bridge suspended over the water.
The trick is to run fast enough across the water, as the rest of the bridge supports the board that is taking the monks weight. As he moves across the bridge, each board he steps on, starts to sink into the water, but its rate of descent/sinking is slowed by the support it gets from the rest of the bridge. If the boards were not connected, then this wouldn't work - each board would sink almost as soon as the monk stepped on it.
Hope this makes sense :)