A VPS stands for virtual private server which essentially means that a single machine is partitioned into separate servers that each act like a dedicated machine. It can be visualized as a number of small servers inside a big server. A VPS runs its own copy of an operating system (OS), and customers may have superuser-level access to that operating system instance, so they can install almost any software that runs on that OS.
For many purposes they are functionally equivalent to a dedicated physical server, and being software-defined, are able to be much more easily created and configured. They are priced much lower than an equivalent physical server.
While VPS hosting is very similar to shared hosting in that multiple accounts are hosted on a single machine, a VPS webhost will guarantee you dedicated resources for your website and isolate your sites from others that are on the same box (physical server). A number of virtual private servers can be installed on a single physical server with each one running its own operating system. However, the user can enjoy certain benefits like dedicated resources, powerful customization options and better security & control.