As for the question "What is a VPS"
A VPS is a Virtual Private Server. It is basic a server that looks like a standalone box but in reality shares the same hardware as many other machines. This can be done using software such as Citrix Xencenter or Parallels Virtuoso. I personally would recommend staying as far away from the Parallels Virtuoso software as in many cases it does not support the latest updates and overall is a pretty crappy product.
As for a home user I would recommend messing around with virtualbox to get a feeling of what a VPS is and the benefits of running one, such as truely optimizing all available hardware to it full potential.
An Example would be setting up a clustered web hosting solution using VPS technology to obtain a super stable solution with minimal hardware.