A grindstone is usually curved out of a thick, porous stone such as sandstone and given a fine grain.  The stone is mounted onto a central axis allowing the grindstone to be spun at varying speeds.  With the grinding process, items such as knives and tools can be sharpened; however it can also be used to polish wood or stone (the fine grain of the grindstone will buff rather than gouge).

Grindstones at Heritage Center
Grindstone at Monticello Utah, Frontier Museum

Wikipedia article on grindstones.