A dedicated server is exactly what the name implies. It's a standalone server that's devoted entirely to you. You have total control over every aspect of the server.
A Virtual Private Server (VPS) is a virtual server contained within a dedicated server. When we create a VPS, we carve a dedicated server into a small number of VPSes. The exact number of VPSes per physical server depends on the VPS specs, but the count is far lower than with a shared hosting package. A VPS will not offer as much power as a dedicated server, but will greatly exceed the power available from shared hosting.
A VPS therefore represents the best of both worlds: You get more power than shared hosting, but at a much more economical price. Think of a VPS as a stepping stone between shared and dedicated hosting.