What Mastercard and Visa do is handle the electronic transaction that the merchants use through their huge network. This is why you will here things like "anywhere Visa is accepted". When Visa gets a request for a transaction from a merchant they verify funds and approve the transaction based on information that your bank gives them.

Once the transaction is completed, Visa will get that amount from your bank and then pay the merchant the money, less their transaction fees. Transaction fees is how Mastercard and visa make their profits. From those fees they maintain the network and promote the brand through marketing and advertising.