Many people are familiar with airfoils. Foil is simply another word for the a wing (such as the wing on an airplane). A hydrofoil is a wing that ‘flies’ in water. Hydrofoil is also used to refer to the boat to which the water wings are attached. A hydrofoil boat has two modes of operation: (1) as a normal boat with a hull that displaces water and (2) with the hull completely out of the water and only the foils submerged.
Hydrofoils let a boat go faster by getting the hull out of the water. 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.
The foils on a hydrofoil boat are much smaller than the wings (foils) on an airplane. This is because water is about 1000 times as dense as air. The higher density also means that the foils do not have to move anywhere near as fast as a plane before they generate enough lift to push the boat out of the water.