Hydrofoils are boats/ships fitted with "wings", better known as foils, which act in a way very similiar to the wings fitted to aircraft.
As a hydrofoil craft gains speed, the hydrofoils lift the boat's hull out of the water, decreasing drag and allowing greater speeds.
In these pictures, you can see the layout of the foils, underneath the ship. the basic idea being that the less of the ship's hull is in the water, the less drag occurs and the more efficient the ship becomes.
Text and Image Source: Wikipedia Hydrofoils
Since air and water are governed by similar fluid equations—albeit with different levels of viscosity, density, and compressibility—the hydrofoil and airfoil (both types of foil) create lift in identical ways. The foil shape moves smoothly through the water, deflecting the flow downward, which, following Newton's Third Law of Motion, exerts an upward force on the foil. This turning of the water creates higher pressure on the bottom of the foil and reduced pressure on the top. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flowfield about the foil has a higher average velocity on one side than the other.
When used as a lifting element on a hydrofoil boat, this upward force lifts the body of the vessel, decreasing drag and increasing speed. The lifting force eventually balances with the weight of the craft, reaching a point where the hydrofoil no longer lifts out of the water but remains in equilibrium. Since wave resistance and other impeding forces such as various types of drag (physics) on the hull are eliminated as the hull lifts clear, turbulence and drag act increasingly on the much smaller surface area of the hydrofoil, and decreasingly on the hull, creating a marked increase in speed.
Although they can allow the shop greater efficiency in increasing in speed for a given engine power and a decrease in drag, hydrofoils do have some significant disadvantages.
Hydrofoils are impractical if they operate in waters that are not perfectly clear of obstructions such as floating/semi submerged objects and large, heavy marine animals, such as dolphins, tuna, seals or whales. If the ship collides with these objects, the light construction of the foil and the struts may give way, creating a risk that the ship may roll upside down at high speed, which has reduced their popularity amongst ferry operators.
Hydrofoils are also relatively expensive to build and maintain.