If you want to use a 'credit' card then that means your spending money you don't have, so you're spending the banks money, that's why you need a bank account, sort of simple but that's the idea.

A 'debit' card is money you do have, and you don't need a bank account for some of those, for example you can get 'pre-paid' cards, you top them up with paper money then spend them wherever.

There's also bitcoins and all the other digital currencies you can use, I think some places even have Bitcoin ATMS now.