A proxy, according to merriam-webster.com, is “the agency, function, or office of a deputy who acts as a substitute for another”
In computing, a proxy server is a computer application running on a server that acts as a middle man between you and another server.
To put it simply, you connect to a proxy server, and then you instruct the proxy server to connect to another server, say 127.0.0.1, and to request the page “index.html” from that server, and give it to you. As far as 127.0.0.1, knows, your IP address never visited them, but the proxy’s IP address has. This means that 127.0.0.1 will not be able to directly track you.
The upside of using a proxy server is obvious: If you’re breaking into a server, or just don’t want people to know you have a foot-fetish, a proxy can help by hiding the fact that you visited a certain server. Proxies are also useful for accessing forbidden sites on school and work computers.
The downside is that the proxy server may be logging everything you’re doing, which means that not only will they likely give you up as soon as the Feds come knocking, but they can read any unencrypted login details you may have sent through the proxy server.
One solution to the first problem is using a proxy chain. This means that instead of connecting to a proxy and then to your target, you connect to a proxy, which connects to a proxy, etc, and then to your target.
This guide is meant as an introduction to the concept of proxies. By no means should you stop here.
Be sure to check out http://en.wikipedia.org/wiki/Proxy_server