What it means
That glorious split-second when your brain finally boots up, the fog lifts, and you suddenly get what everyone's been banging on about. It's the mental equivalent of a cat realising the red dot isn't going to be caught. You'll hear it when someone's been slow on the uptake and then it all clicks.
Usage examples
"I was staring at the maths problem for ages, then penny dropped and I nearly smacked myself."
"He didn't laugh at first, but when penny dropped he was howling for a solid minute."
"Don't worry if you're confused, give it a sec, penny dropped for me just now too."
Where it comes from
Comes from old-school coin-operated machines, like public toilets and peanut dispensers. You'd shove a penny in, and nothing would happen until the coin actually dropped inside the mechanism, often with a satisfying clunk that meant 'right, now we're in business'. That delay between action and result stuck as a metaphor for slow realisation.