Silicon Carbide Cloth is a type of sandpaper. Similar to sandpaper used for wood, the grit adhered to different paper weight/strength, polyester or a cotton-polyester blend (cloth) is powdered Silicon Carbide (a compound of silicon and carbon that in its natural state you may know as 'moissanite'). The numbers of this special paper/cloth determine the coarseness where grits from 400 to 1200 are fine (and may be found at auto repair stores) and the lower the number, the more coarse the abrasive (check a hardware store). Low number grits can remove deep scratches quickly but as they remove metal they will leave less-deep scratches that will need to be removed by using fine and then finer grits.
With relation to jewelry making, this product is generally used to polish brass, aluminum and copper. The paper can be used either wet or dry and can be glued to a block of wood, a dowel, pencil or simply used by hand. (I like an inexpensive emery board.)
Answer contributed by Dale "Cougar" Armstrong