IMO The best mental model for conveying proof of work to a layman is to explain it as a lottery game, where you have to guess a magic number to win.

The magic number is very large, completely random, and unknowable beforehand. The only viable strategy is to guess randomly until you get it.

That is an easy enough game for anyone understand, though it sounds like the most boring game on earth.

However, one upside is that you can guess as much as you want, as quickly as you can handle. So it makes better sense to play this game using a computer, where essentially the most computation wins.

It is also the simplest and fastest provably fair lottery system that you can play amongst computers. There are no ways to cheat and no central authority conducting the lottery. It's just a game of math and computation that a network of computers can play.

So while this lottery may be the most boring game on earth to humans, it can provide great utility for computer networks, and it happens to scale incredibly well.

The greatest example of course (in hindsight) is to run a peer-to-peer decentralized banking system, where computers can compete in the lottery to make updates to the central ledger, in a way that's provably fair across the network.

But another good example is spam prevention, where the lottery is kept fairly easy to play for a single round, but scales very poorly for multiple rounds (i.e a spam attack). Proof-of-work was invented originally for this use-case.

I hope this helps.