covering - an artifact that covers something else (usually to protect or shelter or conceal it)

mat - a thick flat pad used as a floor covering

matting - floor covering of coarse fabric (usually of straw or hemp)

parqueterie, parquetry - a patterned wood inlay used to cover a floor

carpet, carpeting, rug - floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)