A car polish is a product which contains an abrasive which removes a thin layer of your car's paintwork. In this way it will remove dull oxidized paint and can remove some very fine scratches such as wash marks. Polishes can usually be applied by hand or machine polisher, although many professional products these days are specifically designed with machine polishing in mind.
The abrasive can be anything from crushed almond shells to aluminium oxide, with some more modern polishes having disk shaped nano-particles which will 'cut' the paint more depending how much pressure you put on them. Polishes may also have ingredients such as ammonia which have a chemical effect.
Not every bottle of product, which is labelled a polish, is actually a polish. Over the years we have found some very cheap products to be simple waxes, we assume they are using the word colloquially.
Furthermore, some polishes are combination products which will polish and wax at the same time.