There are many credit cards that offer this type of rebate. Some flavors of American Express, and most if not all the ones from Discover. Individual banks offer Visa and Master cards with cash back.
These offers tend to be a percentage back from each transaction. The percentage can vary by the type of store or the amount you charge per year. the amount can vary for 0.25% to 3% or more.
There are terms and conditions, some will not give you the money if you miss a payment; others have maximums. Some companies will offer you additional ways to earn cash by using their site for online purchases, or by turning your points in for store credit at certain retailers.
These offers are different than the ones that offer airline miles, or hotel points.