This is a grinder. The motor is in the middle, and attached to both ends of the motor are a couple of grinding stones, usually a coarse stone on one side and a finer stone on the other.

The grinder

A grinder is used for many different operations, however, most of those operations are best done on a belt sander. If you're trying to deburr a piece on this narrow stone, and you're succeeding in removing any material at all, you're heating up the part and the stone. If you were to do the same job on a belt sander, you'd have more area to work with because the belt is wider, and the whole operation would go much faster. And the temperature of both the belt and the part would be much lower.

The purpose of a grinder is for sharpening tools that are typically made from tool steel. Sharpening drill bits is a common operation for a grinder. The same job can't be done on a belt sander because the belt is more flexible: as the belt comes down across the front of the drill, it tends to move around a little and round off the cutting edge. You can avoid that problem by using a grinder with a very hard stone, so you get a nice, crisp cutting edge.

There are still occasions when you want to use the standard, high-speed steel tool. Maybe you want a tool that you can't buy, such as an odd-shaped file you can't fine in a store. If you have a larger file and a grinder, you can grind down the file to the size and shape you need.