A Balanced Flue is a superior heating device developed in Holland in the 1930's. Whereas traditional heating appliances were 'open' (i.e. they drew air from inside the house to create a fire, then released excess gases through the chimney to outdoors), heating appliances installed with a Balanced Flue draw the initial air from the outside, through a different channel of the same Flue from which waste gases are expelled after burning.
As a result, a boiler or gas fire that is installed with a Balanced Flue is sealed. This makes it more fuel efficient, as less heat is lost by virtue of the fact that there is no open air channel between outside and inside (as with the traditional Flues).