The standard sliding piece puzzle is often called the 15-puzzle. It consists of a square tray containing 15 square tiles and one open space in a 4x4 arrangement. The tiles are usually numbered 1 to 15, or have some kind of picture on them.
Any tile lying next to the space can slide into it, and so the tiles can be mixed up.
This puzzle is often attributed to Sam Lloyd. This is not entirely true. He did not invent the puzzle, but he did invent the 14-15 puzzle, the variation in which the tiles numbered 14 and 15 are swapped, with all other tiles in place. He knew however that this puzzle could not possibly be solved. Suppose the inside of the tray containing the tiles has a checkerboard pattern.