When functions, procedures, calculations or other processing are performed on a server, they are considered server-side. By contrast, client side is on the user's end. A good example of a script that executes on the server-side is a shopping cart or a search engine.
Today, almost all websites and online applications utilize both server-side client side processing.
Note: Server-side processing is typically slower than client side, so programmers prefer utilizing client side programming whenever possible.