Biomass sounds very high tech, but essentially it means burning plants. Burning plants usually means burning wood, and domestic biomass heating is usually wood or wood pellets. Burning wood releases CO2, but this is CO2 that has been recently absorbed by the plants when they grew, so it is not adding to the CO2 in the atmosphere, as long as you are burning wood from sustainable sources.
Wood as a fuel is not completely carbon neutral, as must take into account transport – a lot of wood is grown abroad – but it still scores pretty well in overall carbon emissions.
At the most basic level you can burn logs on your open fire, lovely, but not efficient. At the next level, a wood burning stove can extract much more energy from each log – over 80% being possible for some designs. Collect wood from your own forest, on foot and you have a very low CO2 heating system. If you want to heat water, for radiators or hot water, and things get a bit more complicated, as the water jacket of a back boiler reduces the burning temperature, and the efficiency.
Log burning stoves are not something you can run from a timer, so they win no prizes for convenience.
So, if you want the efficiency and control of a gas boiler but reduced CO2 of biomass you need a wood pellet boiler