A server accepts requests and responds accordingly while a client makes the actual request to access services made available by the server. A server can also be referred to as a mainframe.
The names of these system parts reflect their operations aptly. The name for the instance of software is reminiscent of a server in a restaurant; the relationship between the client and server operates much the same way because the client or customer orders something off the restaurant's menu. The server turns in that order and brings it back to the client. In computing terms, the client makes a request to access software on the server, and the server pulls up the program and grants access to it.