A board press is when you take an actual board or boards and stack them on your chest. You preform it just like a bench press but your only using a partial range of motion. Powerlifters use this in order to work the top end AKA lockout of their bench press.
Usually 2x6's are used. You cut them off about 12-16 inches long.
Most people use anywhere from 1 to 5 boards for variation. Hope I helped.