What the fuck is electricity?

No.14250422 ViewReplyOriginalReport
So we've got those medieval farmer guys with windmills. The propeller thing is connected to gears, so that when wind turns the propeller it turns the gears which mill the wheat or whatever. Makes sense.
Modern day. We've got dams that dump water of gears to turn them. We've got nuclear reactors that boil water to turn propellers with the steam. We've got coal stuff that's basically the same thing.
How do we get from turning propellers to charging phones hundreds of miles away? Are there, like, billions of microscopic gears inside the phone and like the steam ???
How do you store the energy of something inside batteries?
I remember hearing in school that potential energy was metaphorical, you didn't actually accumulate energy from being high up, for example. Is electricity like that too?