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