Gateway

A gateway is a agent or software that terminates a message on an inbound interface with the intent of presenting it through an outbound interface as a new message. Unlike a proxy, a gateway receives messages as if it were the final receiver for the message. Due to possible mismatches between the inbound and outbound interfaces, a message may be modified and may have some or all of its meaning lost during the conversion process. For example, an HTTP PUT has no equivalent in SMTP.
Whew! That will give you a headache! Try our "normal" definition below if you’re still confused.

The above definition of a gateway is courtesy of the World Wide Web Consortium @ Gateway

A gateway is software/program that resides on a third-party server that is responsible for all of the transmissions necessary between the merchant and the processor to complete an electronic transaction.

Gateway Fee
Because a gateway resides on a third-party server, there is usually a flat monthly fee called a "gateway fee" that a merchant must pay to the gateway provider.