What is a VPN?
VPN stands for Virtual Private Network. It's a private connection between your computer - wherever it is - and a computer somewhere else. It's private because it's strongly encrypted, so it can't be read en route.
The University of Edinburgh has a VPN. When you use it, your computer has a private connection to the University's network. To other computers, your computer appears to be on that network.
You should use the University VPN whenever you are working while away from the University, for security.