A Virtual Private Server or VPS is exactly what it says on the tin. It is a server that is divided into a small number of VPS that share resources. Each VPS is completely "private" from the other VPS and functions the same as a regular server.
As a VPS is effectively the same as a regular server you can do everything a regular server can and have much more freedom than a hosting package. As an extra bonus the running costs are significantly lower than having your own physical server as you are sharing a server with other VPS users.