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virtual private server

n. (context computing English) A virtualized server cohosted with other virtual server instances on the same hardware.

Wikipedia
Virtual private server

A virtual private server (VPS) is a virtual machine sold as a service by an Internet hosting service.

A VPS runs its own copy of an operating system, and customers 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, but as they share the underlying physical hardware with other VPSs, performance may be lower, and may depend on the workload of other instances on the same hardware node.