Since this question is broad and ridiculous, here's a broad answer
It could be the OP is not aware IT DEPENDS HOW LONG YOU WANT TO RUN IT FOR.
It's commonplace that if you're living in, say, the Caribbean, you might have battery back up. Imagine a big box the size of a suitcase.
They simply use "car batteries" - maybe a few of them, maybe a dozen of them. And some electronics to make it work.
It will run the whole house fine, but only for a short time -- maybe a few hours.
If you wanted to run a house "for days" it would need an incredibly large amount of battery power - picture "rooms full" of batteries. In the real world it would be impossible and you couldn't do it. But for a few hours - sure, no problem.
So again, what you describe is completely commonplace, you can see it anywhere in, for example, the Caribbean, but it only runs for a few hours at best.
Hope it helps, OP