With a VPS the resources of the server will be split between different websites or hosting accounts.
A dedicated server is a server that’s literally dedicated to your own personal use. You’ll have rights to all of the resources of the machine, and you’ll be able to configure the hosting environment however you wish.
If basic shared hosting doesn’t quite offer what you need and you need a little more control over your host, then VPS hosting could be the right fit for you. If you need a more advanced host with extensive customization options, then check out dedicated hosting.