Let’s take a look at an average heating system without a thermal store:
At some point the boiler starts up, takes a while to warm up its body and get the combustion going really well. Only after this warm-up period its efficiency reaches a reasonable level.
After a while the required heat has been provided, the thermostatic valves in some rooms shut down (because it’s become warm enough there) and the boiler can’t get rid of its heat any more. So it has to reduce its combustion - if possible - or shut off.
After another while the rooms cool down and the thermostatic valves open up again or someone is starting to take a shower or a bath. So more heat is required and the boiler has to increase - or start again - its combustion.
This story repeats itself again and again. Reduced combustion, however, means improper combustion, producing soot, soiling the boiler, the chimney and the air and reducing efficiency considerably.
And if you are the one who has to start and stop the combustion manually, your physical effort is required every time it is getting cool in the house.
Now let’s look at a system with a thermal store:
The thermal store is a heat consumer from the point of view of the boiler and a heat source from the point of view of the house. As such it is always there to “consume” the heat produced by the boiler, no matter whether it is needed by the house at this very moment or not. So the boiler can run at full power for a long time, which means maximum efficiency with a proper combustion.
On the other hand, for the house (and the domestic hot water) there is always a heat source, no matter whether the boiler is running fully, at a reduced level or not at all. So, even when all the wood has burnt down, it doesn’t get cold in the house immediately, and you don’t have to hurry and get the boiler running again.
You can even produce heat in advance (e.g. at night) and sleep late the next morning without your house getting cold.