You may find wood veneer furniture when you shop for older furniture to refinish. Wood veneer is a thin sheet of wood applied over a wooden base. Manufacturers use this method so they can use cheaper wood as a base with a more expensive wood on top. The veneer sheet is simply glued on to the base.
Because of the application, you must be careful when painting veneer or doing any process that allows moisture to be in contact with the wood as it can cause the veneer to buckle and warp. Spray painting is the best way to paint veneer, applying several light coats. You can brush on paint, but again, a couple of light coats are better than one heavy coat.