A service is like a vocabulary (with a particular purpose) that a node can understand. If a node runs a service it means it can understand other nodes that talk to them in that way and is able talk to other nodes in that way. Without the service they don't understand the "words" (and so function) and so don't support it. Adding a service is like adding another vocabulary they can understand, thus adding more functionality.
Network services provide functionality and information dissemination on the network, and a common means of communication between the nodes. An organisation might wish to handle a particular type of network service, like broadcasting a Bulletin, so they install the service on their node, which activates it and allows it to perform the functionality of the service. In the case of Bulletins it will start broadcasting any bulletins you give it on the network.
Network services are the main area of the platform for extending. They can be both public services or private services use for communicating directly with another node without the rest of the network knowing.
Services do not necessarily need to be supported by everyone on the network for them to work between nodes, as individual nodes gracefully handle missing functionality. Custom services can even be built between select nodes if they wish, using the network as a means of operation.