Here's a little map of Client-Server technologies. In this map, hardware is represented in blue.
Software is represented in red.
The client software on the client computer is a web browser or a telnet program. It contacts software called servers on the server computer. So for example, a web browser may contact a web server using the HTTP protocol. The browser sends a request for a particular web page. The browser receives the file and interprets it for the user by supplying images, format, color, and so on.