Bitcoin is a public ledger of agreed transactions. I give you some goods, it's registerd in the ledger that you owe me some number of "thingies". Later someone gives me some goods, and on the ledger I transfer your debt to them, and so it goes round.

At some point, someone offers to give me cash for the thingies registered against my name, I agree and thus they have the thingies, and I have cash.

The clever technical parts are how the public ledger is maintained without there being a central authority, and without having to publicly name the individuals who hold the assets.

I've used that explanation several times to good effect so far.