A virtual server, is an instance of an operating system running on top of a lot virtualised hardware, which is usually shared amongst many virtual servers.
Well, since hardware already interacts with an operating system, like Windows, by using software like drivers, you can make improvised software that appears to be hardware, to the operating system.
This is done by using something called a hypervisor. Which sits on top of your real hardware and allows you to create virtual interfaces. Then, using your virtual hardware and a virtual BIOS. You can install and run a copy of an operating system, on top of your existing hardware. But, because it's virtualised, you can run MANY copies of an operating system and often many different operating systems.
Each instance of virtual hardware, that can run an operating system, is referred to as a virtual server or a virtual machine.
If you know what an emulator is, then this is not a different concept, just applied much more generally.