You store your contact information on the chip. Then, if your pet gets out and someone finds it they can take it to the vet to have the chip read. Then they can contact you and give you your pet back.

You could, of course, have your contact details on their collar. But collars can come off or break. And if you're worried about privacy, literally anyone can just read the tag on your pet's collar. Most people aren't going to have the equipment on hand to read a chip.