Its very easy. Instead of you making a transaction to your supermarket and your neighbor making a transaction to a bakery at the same time the two of you make one big transaction with you and your neighbor paying in and supermarket and bakery getting out. You and your neighbor both have to sign the bundled transaction but nobody from the outside can know who of you payed to where.

Now image the same thing with lots of people and lots of transactions. If additionally to that lot's of transactions come from and go to wallets that nobody knows to whom they belong, and lots of transactions come from UTXOs that came from coinjoins ... the privacy can be pretty neat

melting three gold coins together in order to create three new ones

You and 4 friends each put a 10 dollar bill in a pile. You mix up the pile and you each take one 10 dollar bill out of it. It's now not certain who has your initial bill. (Forget the unique IDs on dollar bills for a second). Not a perfect explanation but it's easy to understand.

In Bitcoin, each UTXO has a tx history. When you join a CoinJoin pool, you mix up your UTXO with other people's UTXO's in a similar way. No one knows who ended up with your initial UTXO, and no one knows which UTXO now belongs to whom.

CoinJoins are however very visible on the blockchain. If you're interested, you should look up CoinSwap. Chris Belcher is working on this feature, which would allow people to swap coins on the base layer without any trace (it looks like a normal tx).

others answered this pretty well

CopeJoin