A Web Proxy is a server which can act as a proxy for all of your web surfing.
Requests for web content that would normally be sent directly to the site you're visiting will instead be sent to the proxy, which will then fetch the data and forward it back to you, maintaining a copy of the data for itself. This is useful in that with multiple users using the same web proxy, should one user visit a particular site before you have, any of the content on the visited site which has not been updated since the previous user's visit will not be fetched from the site again. That content which has not been updated on the site will instead be forwarded to you directly from the web proxy, greatly reducing the time it takes to load a web site since the proxy is almost always significantly closer to you than the site you're visiting.