A hydrofoil is a wing shape attached to a boat. The foils are shaped like an airplane wing, in that it is tapered to allow water to flow quickly over it. At higher speeds, this action creates lift. This, in effect, lifts the boat out of the water and into the air, where there is much less resistance and higher speeds can be reached.
As mechanical engineering students at the Massachusetts Institute of Technology (MIT) explain:
When a normal boat moves forward, most of the energy expended goes into moving the water in front of the boat out of the way (by pushing the hull through it). Hydrofoils lift the hull out of the water so that you only have to overcome the drag on the foils instead of all of the drag on the hull.