This is a kind of test print, which is usually done via printing press to check the quality of printing and the master. It usually shows directly how the result will finally look like. A Hard Proof has the same dimensions as the final product.
Another important feature of hard proof is color checking not only for multicolor printing.
Usually the printer won’t print just one print sheet, but around 10 to 20. This is the chance for the customer to allow very final corrections and alterations. Before printer will start the actual circulation the customer is asked for Imprimatur = let it be printed.
Today the classical hard proof is replaced by different proof versions: soft proof, digital proof. Those are much cheaper.