One can compare a modulating boiler versus a non modulating boiler like a fuse box with a light switch: When coming home in the dark one switches on the light in the hall with the aid of one switch. This will turn on one bulb or two, depending on how many are in the light of course.
But one could as well, instead of using individual switches for the lights, switch on all lights in the entire house at once with the aid of the main fuse. But then all the lights turned on would be a waste of money, one can't be in all rooms at the same time enyoying the bright lamps.
Or compare a modulating boiler with a light dimmer: It can be set to produce an output of light that is wanted, within it's limits of course.
So a modulating boiler produces as much heat as is consumed by the radiators, as much heat as the heating system looses/gives off to the rooms.
Turn on one radiator of 2kWh output and the modulating boiler will produce 2kWh of heat, turn on another of maybe 1 kWh output and the modulating boiler will produce 3kWh of heat. This process of modulating the output of the boiler accordingly to demand happens fully automatical, the boiler "knows" what is wanted.
Versus a non mudulating boiler (which would run on full power and switches off when exagerating the output) a modulating boiler would have long running cycles since it knows when to stop before it's getting too hot (smiley).
And using a condensing boiler is of course much cheaper then a non condensing boiler. But both-the condensing and the non condensing boilers- are build nowadays with a modulating effect.
The worst condenser (energy rating!) can be 10 % cheaper in running costs
then the best non condensing boiler, depending on the heat demand to be compared with. Esp. if fitted with a modulating mechanism.
So for a small house/flat, one where the heat demand can be very low, just one room or so, the choice should be a modulating boiler, and even better a modulating condensing boiler.
If the smalest room to be heated has an energy demand of 2kWh the modulating rage should start at 2kWh. And when the max. heat demand for the entire complex is 30kWh the modulating range for the boiler should be
2-30kWh.
The savings are achieved by avoiding multiple starts, imagine driving along a road and pushing down the gas pedal to get to full speed and then switch off the engine untill the car stands. Then you turn the key and push down the gas pedal again and when reaching full speed you turn off the engine again. And so on. It will get you from A to B but not very economical.