VPS stands for Virtual Private Servers. VPS Hosting utilizes a technology called Virtualization, to create an isolated server that share the hardware of a single physical server however performs like a stand-alone server where you can run your own applications, it can be rebooted independently, has its own full root access, IP's, users, memory, processes, ports, etc. It gives you all the features and functions of Dedicated server, without the additional cost.
VPS gives you the functions and features and of a managed dedicated server but without the price. You have full control of your VPS including full root access to install your own applications not viable on a shared hosting environment. VPS also gives you guaranteed resources, so no matter what, the CPU,RAM, HDD and Bandwidth allocated to your VPS package will always be available for your applications. Since a VPS is an isolated hosting environment it allows you more freedom to run scripts that aren't allowed on a shared hosting environment such as sending out a mailing list and since you get your own mail server you don't have to worry about other users blacklisting the mail server ip, it allows you to create reseller accounts if you are a reseller, and more.