In Australia we call a hearth the piece of non-combustable material that sits under a freestanding heater or at the front of an inbuilt heater to protect the timber or carpet floor. There are many styles available including stone of various types, tile and full slab hearths. Apart from the obvious safety aspects, a hearth adds the asthetic edge and so many modern gas heaters are installed with a floor or floating hearth even when there is no requirement to do so. All woodheaters do require a hearth when the floor is a combustible material.
You can build your own hearth out of brick or tiles if you're handy.