A VPN (Virtual Private Network) is often used as a global connectivity to secure every single data package between your PC and the server. A VPN allows you to redirect all traffic from your PC. A Proxy is a dedicated server often bound to just one application at a time. A VPN can be used for more things and often gives you ability to change between many different countries and IP's while a Proxy is bound to just one.
It's fairly simple to make it so skype doesnt publish your IP, when using it.
Or you can always just set it up with for example a socks5 proxy.
Theres a bit more to it, than just ticking of that box tho. But a step in the right direction.