Wetted surface area is the total surface area of the hull and appendages below the waterline. It should include both sides of the rudder and keel, and if the boat has multiple daggerboards, the given wetted surface area usually includes as many foils as would be used simultaneously.
Units: Area (usually square metres or square feet).
What it's used for
Any surface that's in contact with the water causes drag; frictional resistance depends on how much surface area is in contact with the water. Less wetted surface area generally means less frictional drag.
In a sailboat, frictional drag usually dominates at low speeds, so minimal wetted surface is important to light-air performance. (This is better understood in terms of the ratio of sail area to wetted surface.)
In faster powerboats, and even some sailboats, the hull will climb on plane as it accelerates. Once on plane, wave-making resistance drops off dramatically, while frictional resistance increases. Wetted surface is once again an important factor, but since part of the hull is now out of the water, it's not the same wetted surface as in the at-rest condition!
Wetted surface area is, not coincidentally, the area that needs to be covered by antifouling paint. It's therefore a useful quantity to know when figuring out how long it will take, and how much it will cost, to paint the boat.