A Rocket Stove is any stove / heater that accomplishes both (nearly) complete combustion, and efficient direction of the heat. The Rocket stove gets it’s name by the rush of air (natural aspiration) during the combustion process. It makes a sound similar to a rocket. When the rocket sound is present, the fuel is being consumed at near peak efficiency. This results is no visible smoke and much, much less pollutants than a regular wood stove. This also means that your fuel (wood) will go about twice as far, or rather, half the fuel will do the same amount of work compared to a regular wood stove. This is a major plus in developing countries where wood fires are the the main energy source to cook with. Not only using half the wood with less pollutants in the atmosphere, but also for the health of the immediate inhabitants.
Efficient direction of heat simply means putting the heat where you wish. In a space heating rocket stove, the heat is directed at the top of the stove for maximum efficiency. In a cooker rocket stove, the heat is directed at the bottom of your pan, pot, or skillet. In a rocket oven, the heat exchange is best at the bottom of the oven with your food stacked above.