A masonry stove is basically a very large masonry structure with a tight sealing firebox made of very fire resistant materials. Built into the structure is a highly convoluted smoke path, (which can include a stone oven for traditional baking of breads, etc.) designed to pass through most of the structure. It can have ducts built into it as well, or the heat exchanger for various other heating systems. The basic principle of operation is that you build one or two large HOT fast burning fires a day. The heat from the fires goes through the masonry structure which absorbs and stores the heat while cooling the smoke. The hot masonry structure then radiates the heat back out over the next several hours. This radiant heat is supposed to be very effective and efficient. Masonry stoves are claimed to be very efficient at getting lots of heat out of smaller amounts of wood, and are becoming very popular in Russia and the Scandinavian countries. The basic concept actually is supposed to go back as far as the Roman times when it was used to heat their baths. It was rediscovered in medieval times when increasing population in the northern countries caused there to be shortages of firewood, and a search for stove designs that would give as much heat as possible from minimal wood.
It is worth noting that the operating philosophy of a masonry heater is totally different from that of a normal wood stove. The normal wood stove is designed to run a fairly constant low intensity fire over long periods of time, while the masonry heater is designed to run short, very hot, high temperature fires on an intermittent basis.
A masonry heater is designed to run short hot fires, so it is almost impossible to over fire, and at the same time is less fussy about wood quality, so the use of pallet wood, finished lumber scraps, and other wood that is considered risky in a woodstove is potentially much less of an issue. (It is still not OK to burn treated or painted wood, or other fuels that would make noxious fumes)
The downsides of a masonry heater include are the size, weight and cost. House design is also far more critical. A masonry heater primarily heats by radiant heating, so it is important that it be centrally located in the home, and that rooms to be heated have walls or floors exposed to the heater, or some other other contact with the heater''s surface. To be effective, the structure of a masonry heater must be BIG, so it will occupy considerable space within the home. The size also means a great deal of weight so substantial footings are also needed. These factors, plus the design limitations mentioned earlier, make it impractical to install a masonry heater as a retrofit to most existing structures, and limit their application primarily to use as a designed in feature of new construction. Because of their size and weight, plus the added complexity of their construction, they will cost considerably more to build than a conventional masonry fireplace, but the proponents of masonry stoves claim that they will rapidly pay for themselves with fuel savings.