A gateway is either hardware or software that acts as a bridge between two networks so that data can be transferred between a number of computers. For example, when you send an e-mail to a friend or when you log in to a Web site, there is a gateway that allows the connection take place. Often, your connection to a Web site will involve many smaller connections to other servers along the way. In these cases, a number of gateways are used.
In a completely unrelated story, Gateway is also the name of a popular direct-order PC manufacturer.