When wood burns most of the visible flames are in fact due to gases released by the hot wood. Inside the firebox of a stove the oxygen can quickly become used up and in the absence of oxygen some of these gases remain unburnt and exit up the chimney.
A cleanburning stove generally introduces another supply of air into the firebox, preheated so as to maintain the firebox temperature. This supply of air is often introduced to the firebox through a series of holes which results in jets of air entering the firebox – this means that the air and gases mix well and encourages more complete combustion.
Once a wood stove is running nice and hot you may see jets of burning gas hanging in the firebox where the supply of air enters.