A Silpat is a non-stick baking sheet made out of silicon that is used extensively in baking. Because of the material that it is made of, it keeps baked goods from sticking to the baking surface. It can be used in place of parchment paper and eliminates the need for spraying a baking sheet. It also is a natural insulator, so baked goods don't burn on the bottom as easily.
Never cut on a silpat. While they are dishwasher safe, it is best to wash them by hand. A slightly greasy feel is normal. Store them with paper towels or parchment paper between sheets. When taken care of, silicon mats should last you for many years.