Wait, how can something be greater than a 1:1 energy transfer?
Pretty sure electric translates to heat at a 100% efficiency rating, but that's not considering the 30% or w/e origin of that energy. But I digress, how do you get over 100% returns on your energy?
Well it's because it's not generating all that heat, it's simply moving it from outside to the inside, while using up less energy than it moves. That's why it's not 'efficiency' technically (they call it the coefficient of performance), but it still effectively heats up your house or whatnot with more energy than it consumed in the process.
But that aside, 300% of what? 300% of electric without the heat pump? It's also my understand that heat pumps aren't that great for heating if they are basic above ground units. Have to be the extra expensive dug in ones.
It's compared to the energy it consumes. For example, a COP of 3 (roughly translated to efficiency of 300%) would mean that for every 100 watts the machine uses to move energy, 300 watts are actually moved. As for the above ground thing, it definitely used to be that above ground ones really struggled to work at all when it was below freezing outside, but that was decades ago. Since then we have discovered tricks such as running it in reverse (like you would for air conditioning) to quickly melt any ice accumulation and thereafter keep working, as well as other tricks. They now work reliably even well below freezing, though with slightly reduced heating capacity. That said, putting them underground or underwater is still better for places where it is perpetually cold.
Most heat pump systems do have resistive electric backups in case of emergencies as well, if it really is so cold outside that the heat pump cannot work sufficiently.
As an addendum, most actual scientists would refrain from calling it '300% efficiency' or whatever since naturally we cannot actually create energy from nothing. A heat pump simply steals the extra energy from the outside air (or ground/water). However, I don't think it's misleading to say that in the context of your own home - you actually do get multiple times more out than you put in.
I was actually thinking it as something like:
For every 1btu produced by a standard electric heating unit, 3btu of heat would be produced by a heat pump.
Which, is basically what I understand you to claim. Every 100 watts of energy generates the equivalant of 300 watts of energy.