The network is like a town with a wall around it. Everyone living in the town can already talk to and use the services of everyone else in the town. However, for an outsider to talk to or use any services in the town, they need to access it through a gateway in the wall. Each person in the town can make their own gateway and, through it, provide a means of accessing the services.
Each node can act as a gateway to the network. Acting as a gateway means it exposes Gateway Services into the network, rather than exposing Network Services on the network; the difference here is determined by which side of the node you are on. If you are viewing information that is broadcast on the network through a web page (e.g. on a frontpage of a WordPress site) then the web page, at some point, is using a node to access the network -- this node is acting as a gateway.
Gateway Services tend to be Web-friendly, meaning that they are designed to provide access to services via The Web but really they can be designed to provide access to anything that has Internet connectivity.
Generally every Network Service of a node that shares public information will have a complimentary Gateway Service that can be activated.