A payment gateway is a service that allows accepting credit cards over the Internet. A payment gateway does for a website what a swipe terminal does for a physical store like a Wal-Mart: it encrypts the credit card data and sends it out securely over the payment network. Your 4aGoodCause page will communicate with the payment gateway to process credit cards online.
Most of our clients use Authorize.net as their payment gateway.
More information:
Payment Providers Supported by 4aGoodCause