A sort of "middle man" on the internet. Normally when you go to a website, you send your "request" packets straight to the site's server, and then the server sends "reply" packets back which is what you see as the website. With a proxy, you send your request packet to a server, which then sends a new request packet to the website's server, which then sends back a reply to the proxy's server, and the proxy sends the web site to your computer. This can be used for anonymous surfing on the web. Not all proxys are anonymous, though. Some just edit the packet they send to have your IP address instead of the proxy's, then the reply goes straight to you.
"Someone found out my IP address and gave it to hackers, so I changed it and now I use a proxy so no one can see my real IP."