A VPS is kind of like a virtual computer that lives inside a much bigger computer.
The super duper, big computer can have smaller virtual computers running inside it.
Each of these VPS can have their own operating system and unique complex configurations.
So rather than one big computer with one operating system, the VPS computers appear as stand alone entities, private computers that one can log into and use. No data or information is shared between any of the other VPS that live in the big computer.
Because no data is shared each VPS is private and secure.
One of the cool things about a VPS is that one can increase or reduce the amount of RAM, disk space and CPU that it can use. This way one can run several VPS "instances" on a big computer and they can do their thing without any one VPS using up more resources (power and space) than it has been assigned.
Another cool thing about a VPS is that it fairly easy (when you know what you are doing) to move a VPS (instance) from one big computer to another big computer. This way when a big computer starts getting old and tired one can move any VPS to another brand new super big computer.
This portability is so cool that many people will use a VPS even when they only need one instance on one big computer because it is easier to upgrade the hardware of the server... just by moving the whole VPS to another computer.