In the past, when a user accessed a computer, they were fairly certain that the hardware running their programs was right there with them, inside the very computer they were using. This also meant that every user required their own physical hardware. As hardware capability has become increasingly advanced, it is no longer efficient for each user on a system to have their own hardware. The vast majority of the time, that hardware is idle.
Consider what most people demand of their computer in a work environment. They need their machine to run very quickly for a few moments while they activate programs and pull up information. They then spend long periods browsing information or using a program at less than maximum capacity. A virtual private server is a way to reroute the capabilites of that idle hardware to another user that needs it. This is the essence of the term "vitualization".
Within a virtual private server, one physical set of hardware is present, but multiple computers are accessing it and using it as their own. The only physical hardware that must be copied are the user interface devices like monitors, keyboards, and mice. All of the essential hardware like memory sticks, processors, and motherboards are in a central location and are linked either through a wired or wireleness network to each "ghost computer". Some kind of networking device will likley be needed. A VPS thus creates the illusion that there is more than one computer or set of hardware. Each user will access the hardware as if they were working on a private, independent computer, and they will have full security rights (excepting limitations that may be set by the server administrator) and privacy. They can even run a separate operating system from other users.
On the surface a VPS acts very similarily to a network of linked computers. In a network, each computer is a separate entity, but information is easily shared between the various computers on the network. In a network, each computer is a separate physical entity that is connected to other separate computers through some kind of physical server. A computer linked to a traditional network can be disconnected from the network and still function as an independent system. A virtual private server is different in that it is essentially only a single computer. Virtual machines are essentially computers within computers. They create a separate machine that is utilizing the same hardware. A viritual machine cannot be separate from its parent machine (the physical entity) and still function.
The same privacy, security, and independence that exists when using multiple physical computers is also possibe with a VPS. Privacy is the key aspect that separates a VPS from a standard virtual server as one might find online. All websites and web based programs use servers that may not be private, and it is very easy to access information or infiltrate a machine through the server. That is why most computers have firewalls and other various security programs. A VPS would not need such high security, since it is very difficult to access a virtual machine. A VPS is also not as powerful as a network. In a network each computer has its own processing capabilities and thus can consume many resources without straining the other computers on the network. A VPS will have much higher limitations on storage memory and RAM since only a single computer's resources are availalble. For most business tasks, this is unlikely to cause a problem, but for high end task such as gamining or virtual design that require a more constant supply of computing resources a VPS may not be sufficient.
VPSs excel when deployed as a web based platform. They are commonly used for webhosting, file sharing, and mail sharing, but they can essentially be used for any function. When deciding what to use a VPS for the most important consideration is available resources. How powerful is the physical hardware the VPS will be using and is it sufficient for the server's needs? A file sharing server will require very few resources, but a gaming server will require considerably more.