a proxy is a computer which communicates on behalf of another computer. proxies are frequently used in business networks to create an intermediary between web clients inside the network and web servers outside it.

your workstation sends a connection request addressed to http://www.yahoo.com. your company's proxy server intercepts this request and retransmits it to yahoo's web server. yahoo's web server sends the requested data to your company's proxy server, and the proxy server forwards the data on to your workstation. if all web traffic is forced to go through your company's proxy server, it allows easier application of security measures (such as content filters, virus scanning, etc.).

VPN is a virtual private network -- it is the emulation of private, local network connections over public networks such as the Internet. It is frequently used to allow people working from remote locations to access their company's data network as if they were connected from within a company office.

For example, suppose you use your laptop to establish a VPN connection from a hotel room in Chicago to your company's headquarters in New York. First, a packet of data on the laptop is encrypted. A VPN "wrapper" is attached to the encrypted data (this is called encapsulation) and the whole package is delivered from the laptop to the VPN endpoint via the internet. The VPN endpoint receives the package, removes the VPN wrapper, and decrypts the data. The VPN endpoint then transmits the unencrypted data onto your company's private network. The entire process of encryption, encapsulation, transmission across the internet, decryption, and decapsulation are completely transparent to both your laptop and any servers or other workstations you connect to in the corporate office.

Essentially VPN and proxy servers really don't have much in common, so there is not much basis for comparison. In very general terms, both technologies involve interaction between private, closed networks and the internet.