VPN means virtual private network. The idea is that you can have a private secure VPN operating on top of an unsecure public network (i.e. the Internet). It's a cost-effective secure way to allow students/staff (and no-one else) to access resources on university servers from anywhere.
A simple setup for Monash would be to have a VPN server serving uni resources to any students who are using VPN clients. A more secure solution involves placing a proxy server in between the clients and servers. A proxy server is basically an intermediate system which receives requests from clients and forwards them to real servers such that clients never talk directly to the real servers and all they see is the proxy (more secure this way amongst other things).
Proxies are a pretty general concept though. E.g. you can use a web proxy like
this to anonymously surf the net. By anonymously, I mean that your internet provider knows you're using the proxy but the sites that you access only see the proxy accessing them, not you.
Hope that explanation wasn't too long-winded.