Cerium oxide is commonly used to polish glass. It is typically used in the final stage of finishing to bring the glass surface to optical smoothness. Methods of application include buffing wheels, felt disks on flat grinders and similar processes.
The typical polishing compound works mechanically through abrasion. These compounds leave the glass surface rough -- but the scratches are so small they are not visible in typical uses. Cerium oxide works both mechanically and chemically.
When used with water -- which is recommended for effective polishing -- the cerium oxide contributes to a chemical reaction that actually reforms the molecular surface of the glass. The result is that some of the cerium bonds with the glass to form a layer of cerium silicate that fills microscopic defects in the glass surface (think wood putty). As the polishing continues, the unreacted cerium wears away much of the softer cerium silicate -- leaving the defects "filled" and the surface near perfectly smooth.