Proxy Server
A Proxy Server is a hardware device that offers clients an indirect network connection to other servers. A client will connect to a proxy server and request a connection to another network service whereby the Proxy Server, itself, will connect to that external server to make the request on the client's behalf, capture that external server's response, and relay it back to the client. The response and request could be altered, monitored, filtered, cached, and even outright refused. A proxy server needs to be efficient and highly configurable to handle all the variations of web data and protocols it is called upon to act as proxy for. The quality and methodology of their io caching, plus overall bandwidth of course, plays a key role in the speed at which web communication can progress.
Caching
One application of a proxy server could be to speed up commonly accessed pages. The proxy server, on its own, gathers all of these pages and when a client requests a page that is already cached, it is then able to quickly serve that page directly rather than having to access that external resource. This also, obviously, saves on network resources and bandwidth by not having to repeatedly access the same pages over and over again unnecessarily.
Filtering
A proxy server can also restrict client requests, commonly used in schools and corporations, refusing to serve up pages requested from unacceptable external servers. At a finer degree, a Proxy Server can receive a client's request and pass it through to the external server awaiting a response which can then be filtered depending on the needs of the client or proxy server owner. This can include reformatting for limited viewing sizes such as cell phones and PDAs, security management, virus protection, or selectively removing unwanted components of the results.
Anonymity
A proxy server, as a middleman between client and the external server provides some degree of proxy avoidance. The external server is provided with the IP address of the proxy server and not the client. Some consider this a key factor for anonymity and freedom, others would consider it a way to hide questionnable behavior.
There are many popular proxy server softwares out there from well-known public corporations to small, open source projects.
SSL Proxy
As a side note, there are specialized Proxy Servers to handle web traffic that uses the HTTPS protocol for SSL encrypted tunnels between client and the external server. These Proxy Servers, act as go-betweens for encryption and decryption of the SSL websites. Of course, by installing a proxy server in between a secure communication between client and external server opens a new and possibly unnecessary risk.