To take my previous comment to the next level, have you ever put your finger over the end of an old-school bicycle pump and tried to push it in? If you have, you’ll know that the pump gets hot. The reason is that you are not only compressing air, you are compressing the heat that the air has. This raises the temperature and we can use this phenomenon to move heat around.

Imagine you were outside where it was cool and you extended the bicycle pump and blocked the end permanently.

Then you went inside hour house and compressed the pump. The air (and heat) in the pump would be compressed into a smaller space, so it the air temperature of the air in the pump would increase. If you compressed it a bit, the air in the pump might go up to be the same temperature as the air inside your house. If you compressed it even more, it would get hotter than the air inside the house. If you then held it there, over time, the heat inside the pump would transfer through the wall of the pump to the air in your house. This would cause the air inside your house to warm up and the air inside the pump to cool down until they are the same temperature. In doing this you have taken the heat in the air outside, and released it inside.

If you then went back outside and allowed the pump to extend again, then the air would decompress and, because the heat previously left the air in the pump (when it was inside), it would get quite cold. Colder than the air outside. If you then waited again, the air in the pump would gradually warm up, drawing heat from the air from outside of your house. This happens because even though the air outside is cool, it’s still warmer than the air in the pump.

Rinse and repeat. An air conditioner on heating mode, or a heat pump basically work in the same way. However, rather than using a bicycle pump, they have fluid running in a loop from inside to outside and back inside. The evaporator (outside the house) collects heat by allowing the fluid to ‘expand’ and cool below the ambient temperature outside. The condensor (inside the house) releases the heat by allowing the fluid to ‘contract’ and heat above the ambient temperature inside.

In this way, no heat is directly created from electricity. It is just moved from outside to inside. Believe it or not, this takes less energy than converting electricity into heat directly.

I’ve deliberately not talked about phase change here to keep it simple, that doesn’t change the basic idea behind it.