This man-made abrasive "stone" is used to smooth the edges of glass. The name scythe stone comes from the other (and original) purpose of the stone - sharpening scythes and other cutting blades.
Scythe stones vary in composition. Most common are those made from either aluminum oxide or silicon carbide - two abrasives commonly used for sandblasting glass. The silicon carbide variety of the scythe stone lasts longer and cuts better but is also more expensive.
Stones made from silicon carbide are also known as carborundum* stones. Make sure if someone is selling you a carborundum stone that you are not, in fact, buying a lesser aluminum oxide stone.
Size and shapes vary slightly, though most are bar or block shaped.
* Carborundum is a registered trademark of Saint-Gobain Abrasives, Inc. Saint-Gobain is the latest in a long history of holding companies for Carborundum, the company originally founded by silicon carbide inventory Edward Goodrich Acheson in 1905.