VPS hosting is a type of web hosting that uses Virtual Private Servers. Although the websites are hosted on the same physical machine, VPS allows each website to be fully independent as if each were on its own separate machine.
How VPS works
The easiest way to visualize how VPS work is to use the apartment analogy. Each virtual server, or "container", on the machine is like an apartment suite. You can install any software you like or restart your own container without affecting the other containers on the machine, much like how you can renovate your own suite without affecting the others.
On a shared hosting server, problems with one website might cause the entire server to go down, causing all of the other websites on that server to go down with it. This would not happen on a VPS machine because only the problematic container would go down, but the other containers would be unaffected.
Similarly, some high traffic websites in a shared hosting environment may hog all of the server's resources, thus causing other websites on that server to be unreachable. This would not happen on a VPS machine as each container may only use the resources that are allocated to it.
Why use VPS Hosting?
VPS is great as it slips in nicely and bridges the gap between shared hosting and dedicated hosting services. VPS will give you the independence and flexibility of a dedicated hosting service, but at the price of a high-end shared hosting service.
For users whose websites have outgrown their shared hosting service but can't quite afford a dedicated server, VPS hosting may be the best solution.