Proxy Servers act like middlemen between your computer and a resource (a webpage for instance). Any requests you send to the network will be transmitted through the proxy server. In a similar way, any responses by the network to your requests are transmitted through the proxy server.
However, VPN’s do not work that way. Instead, they encrypt (alter information by using a mathematical algorithm to disable access to unauthorized users) personal data passing through internet wires to hide your identity while surfing the net.