VPS (Virtual Private Server) is a virtual machine created on a physical server. The hosting provider creates multiple VPS on a physical server and provides access to their users. VPS is as good as a dedicated server but with limited resources. VPS provides root access to the user so the user can install any software/OS and perform any root/administrator level tasks.
Having a VPS is similar to renting a unit or apartment in a flat or building. You will have great control and freedom over your apartment without having to share facilities like the living room, bathroom or kitchen with other people. However, you are still sharing certain facilities with the other people in the building, such as the electricity and water systems.