A napkin is a piece of cloth used for wiping your mouth while you're eating or drinking. Your grandmother might insist that everyone put their napkins in their laps before dinner is served.
You can use the word napkin for a fancy linen cloth or a cheap paper one, although in many English-speaking countries it's instead called a "serviette." Napkins have been around since ancient Rome, while some stories have the ancient Greeks using pieces of bread as napkins. The invention of paper napkins dates back to China in the second century BCE. Napkin comes from the now-obsolete nape, "tablecloth."