A virtual private server is a virtual machine which is sold or leased as a service by an Internet hosting service provider. A physical server is partitioned into multiple virtual servers making use of virtualization technology. Each virtual server can run its own version of operating system and acts independently. This somewhat resembles a dedicated hosting environment and as such is most ideal hosting solution for organizations whose need can no longer be effectively served by shared hosting but they lack the resources or the expertise to jump directly to dedicated hosting from shared hosting.
A Virtual Private Server (VPS) is one instance of a Virtual Server. It has its own operating system and install and run all software and applications supported by that OS. A Virtual Private Server can enable you to leverage the benefits of dedicated servers at a cost juts slightly above shared hosting.