A transaction is just a way to tell the Ethereum network that you, as a user, want to execute an action (e.g. sending 1 DAI). A wallet helps build such transaction in a relatively beginner-friendly way.

You have 1 DAI.

Using a wallet's UI (like Metamask), you click enough buttons and fill enough text inputs to say that you're sending 1 DAI to 0xd8dA6BF26964aF9D7eEd9e03E53415D37aA96045 (that's vitalik.eth).

And hit send.

After some time the wallet says the transaction's been confirmed. All of sudden, Vitalik is now 1 DAI richer. WTF just happened?

Let's rewind. And replay in slow motion.

Ready?