A client computer is usually being used to accomplish some sequential task. This might include web browsing, writing software, or operating a machine. The client has an agenda and needs to use services to accomplish it. These services might be data storage, web pages, e-mail forwarding, or communication with other clients.
A server provides a service to any client, and only to clients. It doesn't really use the services for itself.
If there are no clients, the server is idle. If there is no server, the clients can't function.