Virtual private server (VPS)-- is a term to refer to a virtual machine. The virtual machine, although running in software on the same physical computer with other virtual machines, can function similarly to physical machine; having the privacy of separate physical machine, and configurable to run as a server computer. Each virtual server can run its own full-fledged operating system and can be independently rebooted.
VPSs are built on physical machines using visualization technologies which define how the physical resources will be shared among the VPSs. At the moment, Xen and OpenVZ technologies are most preferred. However, only Xen gives a complete privacy regarding CPU and RAM resources. Hence, given a OVZ VPS with 512MB of RAM, we some time could not run a Java program that requires just 200MB of memory. You may refer this video for some more information regarding VPS.
VPS is widely used for web hosting nowadays. A number of VPS providers offer various VPS models (plans) under both the Xen and OVZ technologies. However, very few of them are trustable due to the quality of their products and how their services last.
To date, the top-trusted VPS providers are BuyVM, Hostigation, ramHost. There are some new-born providers doing significant business but for a final decision on whether they are really good, it should takes months or years.