How do I explain current and voltage to a lay man?
Offer him some water (or other beverage) to drink.

What happens when you drink a lot?
You have to pee, which means there's some pressure that urges you to pee.
This pressure is voltage.

Usually people do not pee in suburban trains.
There's a resistance against the pressure.

On a toilet, human brains lower the resistance and there's a flow of pee.
This flow is current.

The water analogy is a very common one (I'm surprised you haven't heard about it) It usually explains voltage as potential energy of water (from what height it's coming from), the current as the amount of water flowing and the resistance as the diameter of the tubing. (or something similar)

People go to great lengths with this analogy, finding substitutes for capacitors, inductors, etc.

You can find a lot of other analogies, because a lot of physics (our world) is driven by a difference in a certain value (different air pressure, different temperatures, ...) and some value changing, lowering that difference (wind blowing, heat exchange, ...).