A program which forwards HTTP, HTTPS and FTP requests, often but not necessarily caching them. (A caching proxy server serves requests from the Cache where possible, to reduce latency and bandwidth.)
Squid is a widely used Free caching proxy server.
Many ISPs and organisations have a "transparent" caching proxy sitting between users and the rest of the InterNet. Transparent proxies take all web traffic and redirect it through a proxy without any knowledge (or choice) of the users. This is not usually a problem, unless the users are trying to measure performance of the network or the proxy is not WellBehaved. In NewZealand, all international traffic incures data charges, so if the ISP can serve you a cached copy, they can save a couple of cents per megabyte.
Proxies are also frequently used in corporate networks, where FireWalls often block access to the outside world, and only proxies are allowed to communicate with it.
Proxies, like WebServers often keep access logs. These logs are useful for debugging, optimisation and maintanance tasks but can also be used to show who is doing what, when and how much it's costing.
See also: ProxyServerNotes
