A virtual private server (VPS) is a method of partitioning a physical server computer into multiple servers that each has the appearance and capabilities of running on its dedicated machine. Each virtual server can run its full-fledged operating system, and each server can be independently rebooted. These servers come with full root access and dedicated resources. There are also many other features of VPS servers.
Often, there are additional fees for backup servers and licenses such as cPanel with a VPS server that you do not have to worry about with a shared server. VPS and dedicated servers also usually include a lot less support in managing the server unless you purchase support. There can be a large technical gap between using a shared server and having to manage your dedicated server.