A proxy is a website designed to get past a web content filter and let people play games in settings where it might otherwise be blocked. Unfortunately, most of the websites which would be fun to check out are all blocked by the school servers. This is what a proxy is for, it's a type of server which pretends to be a real website while letting you surf freely.
What a Proxy Server Does
A proxy server is essentially a portal, letting you look through the proxy to find web content you actually want to see. So if your server blocks a website like Kongregate because it has online games, a proxy would let you play games on the site. A proxy is a legal tool, as this content is not blocked when you're at home. They're most often used to sneak around corporate and educational web filters, useful because some filters are oversensitive. Most proxy sites include a web address field, into which you can type the site address you want to visit.
The web filter on your network may be smart, but it still isn't as discerning as a human user could be. Sometimes it just takes a couple of words to block a website which is either completely innocent, or even useful to your work. For example, a project related to video gaming would probably need information about games, which would likely trip a server-side filter. A proxy server would allow you to get that information for your project without tripping the filter.
Where to Find Proxies
Unfortunately, some IT professionals--who are in charge of these filters--are aware of proxies, and are working to block them. Because proxies are being blocked and created nearly every day, it's difficult to create a static list of them. However, some websites such as TopBits (see Resources) maintain a regularly updating list of the latest 50 new proxy servers. If you have a friend who knows a lot about computers, she may be aware of a few.
Be careful when using a proxy server, because most game websites are blocked because you are supposed to be doing work. If you haven't got a legitimate reason to be using a game website while at school, don't get caught playing around. The most likely outcome is that you'll be told to get back to work, but because a proxy could be used to view illicit materials, it is possible to get into more trouble.