The term "VPN" stands for "Virtual Private Network" which means to securely connect a device to a local network via the Internet.

Never mind where you are, but be securely connected to your home network or your company's IntraNet via the Internet as if you were there -- that's the idea behind a Virtual Private Network. The Wikipedia describes it as follows:

A virtual private network (VPN) extends a private network and the resources contained in the network across public networks like the Internet. It enables a host computer to send and receive data across shared or public networks as if it were a private network with all the functionality, security and management policies of the private network. This is done by establishing a virtual point-to-point connection through the use of dedicated connections, encryption, or a combination of the two.