I like this description. I don't know that you need to explain hashing to laymen, though. Hand-waving is acceptable when communicating to people who aren't skeptics (laymen). If they're really interested in fact-checking you, they can do so on their own time, or you can provide links to detailed explanations.

"It is possible to store passwords in a way that the website cannot see your password, but can still verify that a password entered by you checks out." (trust us, after all you're trusting that we know what we're talking about by reading this stuff)