The basic setup in the client/server model is one device, the server that runs a service and patiently waits for clients to connect and make requests to the service. A 24-hour grocery shop may be a real world analogy. The shop waits for customers to come in and when they do, they request certain products, purchase them and leave. The shop might advertise itself so people know where to find it, but the actual transactions happen while the customers are visiting the shop.
A typical computing example is a web server. The server listens on a TCP port for clients that need its web pages. When a client, for example a web browser, requires a web page that the server hosts, it connects to the server and then makes a request for that page. The server replies with the content of the page and then the client disconnects. The server advertises itself by having a hostname, which the clients can use to discover the IP address so that they can connect to it.