An abrasive is a material, often a mineral, that is used to shape or finish a workpiece through rubbing which leads to part of the workpiece being worn away. While finishing a material often means polishing it to gain a smooth, reflective surface it can also involve roughening as in satin, matte or beaded finishes.
Abrasives are extremely commonplace and are used very extensively in a wide variety of industrial, domestic, and technological applications. This gives rise to a large variation in the physical and chemical composition of abrasives as well as the shape of the abrasive. Common uses for abrasives include grinding, polishing, buffing, honing, cutting, drilling, sharpening, lapping, and sanding (see abrasive machining). (For simplicity, "mineral" in this article will be used loosely to refer to both minerals and mineral-like substances whether man-made or not.)
Files act by abrasion but are not classed as abrasives as they are a shaped bar of metal. However, diamond files are a form of coated abrasive (as they are metal rods coated with diamond powder).
Read more about Abrasive: Mechanics of Abrasion, Abrasive Minerals, Manufactured Abrasives, Choice of Abrasive, Other Instances of Abrasion