A VPS is a virtual private server. This means that it is a server that runs on a virtual machine. A virtual machine is a computer that is run in a virtual environment. This means that the virtual machine is not actually running on a physical computer.
The virtual machine is run on a computer that is specifically designed to run virtual machines. Instead of having a single server that is used to run all of your websites, you would have a VPS. A VPS has an IP address.