Wood that has been exposed to water will discolor. If the water penetrates only the finish, the wood turns white. If the water penetrates deeper, the wood can darken. This is typically the result of a reaction with tannic acid in the wood. It's worse on oak, which contains a high level of the acid, but dark discoloration will also appear on almost any species. Lots of people use a special bleach to remedy dark discoloration, but if water has already penetrated the finish, bleach isn't the answer. Sanding is the best option.
Attach 100-grit sandpaper to a hand sanding block. Sand the surface of the dark spot, including the surrounding area. If it's a tabletop, sand the entire surface. If it's the arm or back of a chair, part of a molding or any part that's isolated, sand the entire part.
Sand with strokes parallel with the grain until the finish is removed, changing the paper on the hand block as needed. When the finish is removed, focus on the darkened area, using more pressure and shorter strokes, tapering the sanding area from the center of the darkest spots to the perimeter. Continue in this manner until the dark area is gone.
Sand over the area again to remove any depressions that you might have created by focusing on the dark area. Attach 120-grit sandpaper to the hand block. Sand the area again until smooth.
Apply a matching stain to the sanded area with a soft cloth and wipe it off immediately with a dry cloth. Allow the stain to dry. If the wood is natural or contains no stain, skip this step.
Spray the wood with a light coat of aerosol lacquer from a can. When the lacquer is dry, sand the wood with a folded piece of 120-grit sandpaper. Spray another coat of lacquer on the wood to finish.