Not the kind for surfing porn (Henry) on the school network but it's somewhat like that. A proxy server handles all packets moving out of the network. They can dissect a packet which allows you to filter what packets move in and out of the network based on keywords and can even scan for viruses although the more thorough the slower the network will be. Proxies can also hide the I.P.s of computers within the network so hackers can't target a specific machine.
An HTTP proxy is the kind we all know and love. The way it works is a client is configured to sent all HTTP requests to the proxy so when a client accesses a website the request is sent to the proxy and then returns the website to the original sender. This can be useful when you need to get around restrictions like region or network based. An HTTP proxy can also be configured to cache web pages so bandwith isn't wasted on frequently requests web pages. Pretty much everything said applies to any kind of proxy like an FTP proxy.