While a relatively new invention its principle of operation can be traced back millenia, and the best operational example of the rocket stove principles are the Roman Hypocaust heating systems.
Rocket stoves work on a very simple principle which is that of having an "L" shaped steel or other heat resistant pipe which is a single piece and is permanantly fitted to a container and is packed with a heat resistant insulating material such as vermiculite; the vertical pipe is called the flue or chimney and the horizontal pipe is called the feed pipe. The feed pipe is split into two by inserting a shelf to divide it into an upper and lower section, on the upper side of the shelf you put your fuel which can be almost any organic material such as wood, and the lower half is left empty for it to draw air.
When a fire is lit most people use a little paper and light it and push it along the shelf of the feed pipe and into the bottom of the flue pipe and then add a little more unlit paper and push this along, the hot gases flow upwards and this draws air in through the bottom of the feed pipe and warms the flue, fuel such as small twigs are pushed along the shelf of the feed pipe until they are in the flames and physics takes over, as the heat rises it draws more air into the fire and it burns hotter, more heat rises and it increases the combustion temperature. Insulating the flue pipe ensures no heat is lost and this insulation maintains heat in the flue and maintaining this heat is crucial to it being such a clean burning unit due to complete combustion.
As the fuel is packed into the top of the feed pipe and pushed along, it nears the heat in the flue pipe and timber and most organic materials emit something called wood gas; this wood gas is drawn along the feed pipe and into the flue where it burns and increases heat.
Rocket burners can be made in any size and used as either a cooker or if a thermal mass is added instead of insulation it can be used as a heater for garages, greenhouses, or workshops; they are commonly being adopted in third world countries as multi function units where they are used as the primary source for cooking, and also by adding clay or clay/pebble mixtures they are fired up and used for cooking and once cooking is completed the thermal mass emits a constant heat for many hours. Basically they are a modern version of the old electric storage heaters which used an electric element to heat up a mixture of oil and stones to a pre-determined temperature then they shut off and the oil and stones acted as the thermal mass and released their heat slowly over many hours, anyone lifting one of the old storage heaters will understand because they were so heavy due to the stones which made the thermal mass.
Rocket stoves are becoming popular due to their efficiency, instead of spending hours cutting firewood and chopping it into logs; the rocket stove uses very small quantities of fuel and releases an enormous amount of heat for very little fuel, and they use smaller fuels such as twigs, leaves, bark, and even pine cones or rotted horse muck, basically they use things most people would ignore and this is what makes them appealing to expeditioners, outdoor types such as campers or fishermen. If you have any organic material you can light a fire and cook, you will need a little paper and a few tiny pieces of wood to light it initially though, from there you can add anything organic which will burn, a friend who is a fisherman has one made from a catering tin of Nescafe for the body and the flue/fuel pipe is made from 60mm diameter stainless steel exhaust pipe for durability and the insulation is perlite which is an excellent insulator and readily available from garden centres, and cheaper than vermiculite.
The largest rocket heater I have made uses the large 47Kg gas bottle and 12" (305mm) thick wall pipe and is used for heating a 40' X 20' brick garage, this has an additional port in the top of the feed pipe at an angle to make it an autofeed unit, the pipes were inserted and the flue pipe was left standing proud so a chimney flue could be attached and the insulation is a mixture of small gravel and liquid clay. Once the pipes were inserted into the bottle a hole was drilled in the top to house a 1" BSP socket which was welded in and a 1"BSP blanking plug was to be inserted once filled, the 10mm gravel was poured in through a funnel until it was 2" below the top and a mixture of clay and water were thrown into a concrete mixer and mixed until it was very watery, this was then poured in and left to settle, then topped up until it was about 1" below the top of the bottle.
One important safety note:
If you intend building such a unit and intend using any wet insulation or thermal mass materials such the gravel/clay mixture or concrete then leave an air space at the top of the bottle and do not seal them up fully as they generate enormous heat and they can explode, I drill a vent hole of 3mm diameter in the bung before fitting it so the wet materials can dry and the air can expand and vent, and contract safely.
This doesn't apply if you use dry insulation such as perlite or vermiculite.