Virtual Private Servers or VPS as they are commonly called are a form of web site hosting that is usually based on some form of server virtualisation such as Xen, Virtuozzo or OpenVZ.
VPS are generally a virtualized host operating system, rather than virtualized hardware (such as VMware), this allows for a higher level of density and efficiency and subsequently VPS are relatively inexpensive. This density however comes at a cost usually in the form of performance especially under high load as VPS do not have dedicated hardware.
VPS are mostly used for web site hosting, email, ERP and CRM applications.