The sweet irony of Reeves being in mnemonic, the matrix, etc. is that he doesn't even own a computer, and has no desire to get one.
Anyway, for those wondering, a squid proxy lets you cache data from the internet for an internal network - or even an ISP. When a user requests a page, the proxy will do the actual downloading, then send the results to the user. The proxy can then store a copy locally. The next time the page is requested, the proxy serves the local copy without having to request it again. There's more to it, but this is basically what it boils down to.
A reverse proxy works the other way around. The users connect to the proxy (which looks like a web server to the end user), which in turn requests data from one or more servers that run behind it. It too can cache data and serve it without requesting it from the actual web server.
This isn't top secret stuff (squid proxy is open source - you can google this info if you wanted), so I don't think it's an issue for me to explain.