The reason for a business to want to accept cards is that some fraction of your customers would choose not to buy whatever it is you sell if not for the convenience. Whether that's a guy who decides not to buy donuts because then he won't have even to buy more scratch-offs or the woman who doesn't get those bald tires replaced because if she did the family will be leaving on cheese sandwiches until payday.

For the consumer the reason is that this is revolving credit. If you pay next month you can have stuff today. That's a small relief, unless it turns into a carried balance and then it's an ongoing burden, but you don't think about that burden at first because you're naturally optimistic.

> If you pay next month you can have stuff today.

There is value in this even if you always pay your full statement balance every month.

If you have a stable source of income knowing your credit card payment is due on the 7th of every month means you don't have to monitor your checking account's balance for every purchase. You only have to think "make sure you can cover $X by the 7th".