What does polishing a car do?

A car polish is an abrasive product that removes a very thin layer of your car's paint. A professional will use a polishing compound on a polishing pad which is, its self, abrasive. A machine polisher will remove the top-most layer of dead paint (clear coat). 

Because polishes are themselves are abrasive, they are causing scratches in order to remove the scratches. Therefore, it is easy to leave buffer marks which appear as smears when seen under the right light conditions. The skill is to use ever finer polishing compounds in order to reduce those scratches to the point when they are invisible.

When done skilfully with a machine polisher, this will also buff out all fine scratches, leaving your paintwork shiny and smooth.

In the past, waxes would be applied over a polished finish and these would fill and hide any buffer marks, and so the amount of work and skill level required to polish a car was less. Ceramic coatings need to be applied directly to the paintwork which needs to be cleaned of any oils and waxes which might hide buffer marks, and ceramic coatings do nothing to hide scratches, so the final stages of polishing a car which are being prepared for a ceramic coating are critical.