From USNews and World Report via Geology.com:
Researchers have discovered the mystery of what produces a polish on the surface of a diamond. They believe that during the polishing process a liquid-like layer of carbon atoms forms between the gemstone and the scaife. Then sharp pieces of grit scrape through the liquid layer, exposing carbon chains to the air. Then as oxygen in the air pulls off carbon atoms to form carbon dioxide a smooth surface is left behind.