Walk off mat is an industry term for a door mat -- what most of us would call a welcome mat, but usually without the "welcome". While this is a general term that covers a wide range of mats, if one is using the term walk-off mat, one is probably refering to a heavy-duty, over-sized, and industrial strength door mat.
The 'walk off' refers to the primary purpose of the mats: to absorb water and mud and wipe off dirt without having to stop and scuff your shoes clean. This means that the mats have to be fairly large -- so that they come in contact with a person's shoes 2-4 times as they enter the building -- and heavily textured, to knock off and trap particles.
These mats are most commonly found in one of two types. Scraper mats are made of a hard but non-slip material such as rubber, polypropylene, or vinyl with ridges or nubs to scrape off debris as you walk across them; these are generally placed outside of entranceways, and are weatherproof and very rugged. Wiper mats are carpet-topped, and absorb moisture and small debris; these are generally placed inside an entranceway. Most commercial and public buildings will use these two types as a set.
While these mats are nominally there to keep the floors clean and dry, they have a more important function; by keeping floors dry and free of mud, they prevent slips and falls, which are disruptive, dangerous, and open the buildings owners to unwanted liability. Insurance companies may require them, and if they don't then common sense often does.