A mat is a hard floor covering that generally is placed on a floor or other flat surface. Mats serve a range of purposes including:

serving to clean items passed over it, such as a doormat, which removes dirt from the soles of shoes
protecting that which is above the mat, such as a wrestling or gymnastics mat, or an anti-vibration mat
protecting that which is beneath the mat, such as a place mat or the matting used in archival framing and preservation of documents and paintings
providing a regular or flat surface, such as a cushioned computer mousepad