A multi-component floor mat that, in one embodiment, is comprised of a first base or frame portion, intended to be positioned on the floor, that is dimensioned to accommodate a second flexible textile mat or rug portion that is releasably held in place on or in said base or frame portion by a plurality of magnets associated with one or both portions, thereby allowing for the easy removal or replacement of the textile portion of the mat and the economical laundering of same.