Back boilers work on a very simple premise. Fires dissipate energy in the form of heat which means that they can be used to heat anything and everything. Water, believe it or not, does fall into that category. When a backboiler is made, there is a reservoir filled with water behind either a traditional fireplace or a stove. When the fire is lit, the water warms up and begins to gain energy from the fire. The water takes the heat energy from the fire and converts it into kinetic energy (energy of motion) thus making the water move. Eventually this someone had the idea to use this moving water and send it throughout the house via pipes connected to the reservoir behind the fireplace or stove.
As the water travels through the pipes throughout the house, the water radiates heat and warms up the whole house. As the water would cool down it would cycle back in the reservoir only to be heated up and then sent throughout the house again. This does however come with its risks. First generation backboilers would have a tendency to explode if not watched under tight supervision. If the water gathers too much energy from the fire, the pressure inside the reservoir and pipes can get too high causing the reservoir to explode. This is the exact phenomenon that happened to early steam engines before release valves were added into their design.