Definition:
VPS is an acronym for Virtual Private Server.
A VPS Web hosting plan means you share the physical server hardware with other websites, but you are allocated a dedicated slice of the system resources.
A VPS is a good bridge between low cost shared hosting and getting a dedicated server. Here is a list of reliable VPS hosting providers.
Examples:
Top VPS server management software include VMWare, Virtuozzo, and Xen.