The trick is that heat pumps are using energy to move heat. Let's make an example calculation: When heating your house to burn coal, you release 1 Joule when b

The trick is that heat pumps are using energy to move heat. Let's make an example calculation: When heating your house to burn coal, you release 1 Joule when burning the coal. It's a small plant, so it is not very efficient. You probably get 0.85 J of heating out of it. If we instead burn coal in a large-scale modern power plant, we release the same 1 Joule, but capture 0.95 J of it in electricity. Let's say we lose 10% transporting it to your home, leaving 0.855 J remaining. Now, we use that energy to move heat from outside into our home, at an efficiency of about 300% - so for every joule we consume, we move 3 joules of energy. This means our house is heated with 2.565 J. But the energy the heat pump consumes doesn't disappear - it becomes heat too. So your house gets a total of 3.42 J hotter! So 1 J of coal gets you either 0.85 J of heat by burning it directly, or 3.42 J of heat by burning it in a power plant and using a heat pump. And of course don't forget that for climate reasons it is trivial to replace that power plant with a solar farm or wind turbine. The worst-case scenario for a heat pump is that it is exactly as efficient as burning stuff directly. But in virtually all cases, it is way better.