it kinda maskes your computer's identity, so that when you browse to a page on the web, it actually appears as if the proxy machine is doing the browsing. So if I came to dnbforum.com without a proxy, it would log my ip address (the little IP: logged thing in the bottom right of all the posts) and cookie (kinda leave a file behind with username/password/settings etc.) my computer. If I do it through the proxy server like the one linked up there, the proxy server's ip address would be logged and it would be cookied. Thus, it masks your identity. Corporations use proxy servers internally to allow computers behind it (that is, inside the network behind the protection of the proxy server) to access the internet. I used to use one when I had a shell account and a 14.4 modem to surf to different parts of the internet that my shell-provider blocked at its routers, such as p0rn newsfeeds and renegade BBS. I could use it in conjunction with some online network tools to h4x0r someone's computer or website, flame someone (don't know if I should be telling you this!), or post on forums as someone else, and be virtually untraceable in all instances.
sorta. most proxies are open on the inside, not on the outside, for just such reasons. Anonymous internet proxies are rare these days - there are a lot of pay ones though, such as http://www.anonymizer.com/index.shtml , that attempt to offer anaoymous email, surfing, etc. On the same note, www.hushmail.com offers free, anonymous email accounts.