Virtual Private Servers are remote computer options to control a graphical user interface or command line console environment. These computing instances run on their own operating system and a great range of these are available. They function as in equivalently to a dedicated physical server and are normally pre-configured then compiled or installed with the click of a button after setting some options within a client dashboard.
Typical PuTTY instance
Depending upon the configuration, some remote connections will require an SSH key, some can be connected to with software such as PuTTy whereas others can be controlled with a mouse, keyboard and graphical user interface as if the machine was right in front of you.
They are price comparatively lower than a physical machine but are often on a shared resource basis and as such performance may be lower, unless you go for the more expensive dedicated server option.
Typical VPS Windows instance
There are many VPS providers but at the same time, you get what you pay for.