VPS stands for virtual private server. The best way to explain this is that you can have paid hosting that is managed such as BlueHost.com. Then you can have dedicated servers where you have your own server, you share it with no one and you pay quite a bit for it too. The happy medium for these two types of hosting is VPS web hosting.
With VPS web hosting you are in control. The server is partitioned off so that you have your own section. You get to choose what operating system you use and you probably want to have some knowledge of Linux or whatever system the VPS web host uses.
So how do you know if you are ready for VPS? If your shared host does not offer you all of the features you need but dedicated hosting is too much money and too many features then you will most like benefit from virtual private server hosting. More often than not personal websites would not need this hosting but for small business owners it is ideal. When you own your own business it is easy to have several websites and if this is the case then you will want VPS because shared hosting will most likely not let you host multiple domains. Shared hosting usually has too many limitations for small and large business owners.
VPS hosting usually starts in the $29 per month range. The prices vary with the features but you easily get what you pay for. This is a great investment for any business owner.