To see the possible win, consider a common Web activity, downloading a new version of Netscape Navigator. Multiple folks in most organizations have downloaded it, so those groups have wasted bandwidth moving the same bits. Many groups solve this problem by having someone download the software late at night and put it on an internal server from which others can fetch it. A better solution would be to have a machine that caches the result of the first download request and then services all subsequent downloads from a copy in its local storage. That's a proxy server.
Proxy servers can also cache Web pages or anything else from the Internet.
Proxy servers are invisible to users, who just receive online items more quickly than usual. Proxy servers do need to see all requests to manage their caches well. They must also update their caches often enough that users always see adequately current copies of the material they access. A proxy server can even do more. For example, it can pre-fetch during times of light activity all the pages a cached page references.