What does it mean by "the penny drops" and how to use it?
Is it an old-fashioned idiom?

Question

Answer

If you have a hole in your pocket the penny drops a lot.

Answer

Yes it is old fashioned. More examples:
I wondered where I had heard the song  on the radio before and then the penny dropped! I actually had the CD.
It takes some students quite a while to understand algebra and then one day, the penny drops!

Answer

It's still used today =]

When the penny drops, someone belatedly understands something that everyone else has long since understood.

Example - I sat and thought for a moment and then the penny dropped.