Virtual Private Servers also known as VSP is a virtualized server created on a dedicated servers, in other words you can say a VPS is dedicated server in a shared hosting system. When you buy a VPS server it provides you a dedicated website hosting environment in a shared server. People running websites with high traffic should prefer VPS Hosting instead of going for shared hosting services. Instead of renting a dedicated server you can get almost same features by rending a VPS in low price compared to price complete dedicated server. There are many types of Virtual Private Servers are available with different features. There are main two types of virtual private servers.
VPS (Virtual Private Server): most popularly comes with OpenVZ, in reality is only a virtualized instance of the operating system being run a main dedicated servers. Resources in this environment are isolated but at some point they are shared. For example an instance / account are assigned 1GB RAM, it will get assigned 1GB of RAM but still it will remain shared in reality.
KVM (Kernel-based Virtual Machine): is relatively less popular as compared to OpenVZ, this kernel based virtualization is actually isolates resources and there is no change of sharing memory and other resources. In the case of KVM you get your own kernel which in the case of OpenVZ is not available to you. In KVM you have complete control on the hardware but in this case you have lots of responsibility on yourself too.