Polish is graded the same way as symmetry by most labs: Excellent, Very Good, Good, Fair or Poor. Just as hardwood takes a better polish than softer timbers, diamonds hardness makes it the absolute leader in luster.
Poorly polished facets may and can reduce the intensity of light reflected from, or refracted into and out of a diamond. Labs assess polish by examining the diamond, facet by facet, with reflected light with a microscope; you or I may not see any difference without the correct tools.
Because the major labs have no cut grade systems the market has read more into Polish (and symmetry) simply because it is there on the report. GIA has announced that when they do release their Cut Grade system, diamonds with Excellent and Very Good polish grades will make it into their highest cut grades. Tests have shown that none of the expert observers they used in their study could detect any difference between VG and Ex.
A common polish defect is surface grain lines. When as they polishing each facet even the most skilled cutter can encounter variations in hardness or grain, just like with timber. The result is very fine polishing lines running across a facet. These grain lines are very common in pink and fancy colored diamonds, but are rarely visible to the naked eye.
If you choose a diamond with an SI or VS inclusions, a few microscopic polish lines may be of no relevance. But if you were considering buying a Flawless diamond, then excellent polish may be a consideration.
If the polish is rated as fair or poor, visual performance may be noticeably reduced, or you may be able to see a polish line on the crown of the diamond.
Polishing lines. From 3D Diamond Course. Courtesy of OctoNus.