A VPN is a virtual private network, which commonly is used to provide a secure tunnel across an insecure public network. The biggest of these is of course the internet, and a VPN is the primary method of ensuring some security and privacy when using this vast, global shared network.
There are lots of VPN providers, although most large companies set up their own connections. This involves usually client side software (although Windows has client software included) plus a Remote Access Server to receive the connection. This would normally sit in a DMZ on the periphery of the internal network.
This means that remote workers would have access to all the facilities, documents and applications as if they were sitting in the office.