I've mentioned Bitcoin many times now only to have someone who doesn't really "do computers" say they don't really understand what Bitcoin is... and, due to them needing a nice non technical answer and me not fully understanding how crypto currencies work myself, I've been kinda stuck for an answer.
But here's my latest try and it should work for at least a limited part of "my audience".
Imagine you have a sudoku... once it's finished you can check you've got the right answer really really quickly... it's easy peasy to say "yes, you have solved that sudoku!"... but the actual solving of it takes a long time and quite an effort. You could say that that sudoku is "worth" the amount of time that it took to solve it.
Now imagine that you have a gigantic sudoku... maybe 10 million squares across and down. A person couldn't solve it, it'd just take their entire lifetime.
A computer could solve it! But it wouldn't be able to do it quickly and it would take a long time and a lot of electricity. So once it's finished you could say it was "worth" the amount of electricity your computer has used to solve it.
With all these people getting their computers to solve new massive sudokus. After a while you would also run out of sudokus to solve... someone else will have already done the one you've thought of.
So you've ended up with something that took a lot of cost to produce that are in limited supply. And in the same way that you could choose to trade by swapping goods for, say, a genuine picasso - you can also do a trade for a puzzle that cost stupid amounts of electricity to produce.
I've completely ignored how the blockchain is used to transfer "ownership" but most of the people I've been talking to are stumbling before we get to that.
For which I'm, frankly, glad because again, I don't really know what I'm talking about myself and, more importantly, don't care enough to find out. I'm just looking to provide a simplistic answer to a difficult question.