Also known as a Virtual Dedicated Server (VDS), a Virtual Private Server (VPS) is, essentially, a server that has been divided into a number of virtual computers. Each virtual computer has a certain percentage of the resources of the entire server, and to a user, there's no discernable difference between a dedicated server and a VPS - apart, of course, from the fact that virtual servers will have lower specifications.
Virtual Private Servers are great for people who want the control and freedom of dedicated servers, but don't want to pay the high prices associated with them!