A process and service that automates payment transactions between the shopper and merchant. Classically refers to credit card transactions, but nowadays the term describes also internet payment methods like Paypal.
It is usually a third-party service that is actually a system of computer processes that process, verify, and accept or decline credit card transactions on behalf of the merchant through secure Internet connections.
See also: http://www.firstatlanticcommerce.com/resources/payment-processing-diagram.aspx Authorize.Net: How it Works (Diagram)