Sir,Why do we polish diamonds?

So that more light could reflect back and the diamond would hence shine more. Before polishing, some surfaces get rough due to abrasion by other hard surfaces or due to natural occurance in a state with rough surfaces. So, less relection of light falling on its surface occurs. By polishing, diamonds get a smooth surface. To enhance further the shine, sharp cuts and edges are made over the diamond which gets the light to travel inside and reflect through more surfaces of the diamond giving the diamond an illuminating and shining effect.

TIR phenomenon it amplified by the cuts that are made on the diamond(There is a whole industry in India based in Surat, Gujarat for cutting diamonds).
COnsider a metal vase with smooth surface. initially, it has a lustrous surface which is the basic property of metals. With time, the surface gets rough or may be corroded if not protected. This causes the surface to lose its shine. Almost same thing happens with time.

The rough surface is polished to get its outer shine back which is very rare.

So the TIR takes advantage of the cuts on the diamond such that more light suffers TIR making the diamond shine even in low light.