A virtual private server (VPS) separates you from other customers on a physical web server, running on a copy of its own operating system, but it shares CPU and RAM resources of the physical web server with other VPSs running on that server.
A dedicated server, on the other hand, is a physical web server leased and controlled by the end client, without sharing physical CPU and RAM resources with other sites. Its very much like owning your own server, without the huge capital asset investment.
Most hosts offer a mix of unmanaged versus managed services for dedicated servers. Unmanaged plans typically offer the basics – the hardware, operating system, control panel and Internet connection.
In a VPS, a single physical server is partitioned so that it appears as multiple servers. The physical server boots normally, then runs a program to boot each VPS within a virtualization environment.
With a dedicated server, you have more flexibility and control. Dedicated servers have historically been the server of choice for complex business or high end eCommerce sites, but have recently become very popular substitutes for VPS servers and less complex solutions.