A cash-back credit card functions like a normal credit card, except you will get a rebate on goods you purchase using the card. This is what can make them a little more attractive than your regular credit card.
The terms of cash-back credit cards vary from card to card. Some cards limit the type of goods which are eligible for rebate. So, for instance, you might have a Shell cash-back credit card, and only purchases made at a Shell gas station are eligible for a rebate. This is the most limiting type of card.
Other cards may give you small a rebate on all purchases, but give a bonus rebate on certain purchases, like groceries or gas etc.
Rebates on cash-back credit cards vary as well, but most are 1-3% of the purchase price of qualifying items. Some cards may run promotions where they give an additional rebate on some items for a short period of time. Also, some cards may have a maximum rebate limit, while others may have no limit.
A true cash-back credit card will give you a cash rebate (either by check or as a credit on your bill, whichever you choose), but also included in this category (are the points of most banks) are rebate or reward cards, which may give you goods or vouchers in lieu of cash.
A common example of a rewards credit card are those issued by airlines, which give the consumer airline miles instead of cash as a rebate. Some cards may offer the choice between getting cash back or getting a voucher or gift.