The pinblock is the block of wood into which the tuning pins are set. It sits behind the metal plate. The pinblock is a plywood strip (usually at least 7-ply) of extremely hard wood (usually rock maple). It is plywood so that the wood is the same strength in every direction. This great reduces the chances of splitting. The wood needs to be hard, so that the tuning pins are held tight enough to withstand the string tension when the piano is brought up to tune. (to give you some idea, the collective string-tension of an in-tune concert grand is about thirty-three tonnes!).
Below: A picture of a multi-ply pinblock. Notice how deeply the pins are set into the wood.