If there's a small cloth under your plate and silverware when you sit at a table, you can call it a place mat. If you are eating at a diner, your place mat is probably made of paper and covered in ads. If you are a kid, your place mat is probably made of plastic to protect it from your spilled milk.
Some tables are set with only a tablecloth, while others might have individual place mats instead of (or in addition to) a tablecloth. When you set the kitchen table for a tea party, you might carefully arrange place settings on a fancy place mat for each of your guests. Place mats come in different materials, shapes, and sizes — although they're most commonly a rectangular piece of soft fabric — but they're intended to keep the table tidy and protected. At a casual restaurant, you might have a paper place mat printed with the menu, or with games meant to entertain children.