These organizations provide accounts to merchants who desire to process cards.  This is achieved through a formal Agreement between the Acquirer and merchant.  The Acquirers can be one of several profiles:

1 - A "Merchant Services" division of a conventional brick and mortar bank

2 - An Independent Sales Organization (ISO) reselling the services of a major Acquirer

3 - An independent company without conventional banking services

Regardless of their profile, all Acquirers buy the transactions from the Merchant based on "discount" rates defined by the Card organizations called "Interchange Rates".