A server is, effectively, a specialized computer that is connected to a network and accessible by clients to do specific tasks. Generally speaking, this allows a single machine to “serve” applications to multiple other machines, which can ultimately reduce cost, as well as make application maintenance easier (by providing just a single point of maintenance for the network administrators who work with the equipment). A server can help a company with many different tasks, whether running specialized reports, or keeping content in a remote database. In short: the server will do exactly what it is told to do; just as a computer would. But they are typically highly specialized and will do that specialized task very well, as it does not have to allocate resources to other functions that might remain unused.
A VPS, or Virtual Private Server, is a “virtualized” version of this physical machine. When a user connects to a VPS, they do not see the actual “whole” dedicated server. Instead, they see what is called a “virtual machine“, which is basically a completely usable shell of the operating system that makes certain resources available to the VPS user without allowing access to the actual physical “root” of the machine.
This virtualization allows a single physical server to have several instances of an operating system running simultaneously, all accessible by different users for each user’s individual purposes.
In a sense, a Virtual Private Server gives greater control to the owner of the VPS partition without the potential to mess up the entire server. Each instance, then, can be programmed independently of every other instance, and can have their own individual administrative users to run the VPS instanced operating system.
The primary advantage of a VPS over a traditional shared web hosting environment is speed, primarily. There are a far greater number of websites hosted on a standard shared host than there would be on a virtual private server. Since the VPS will have fewer users on it, the website’s performance on a Virtual Private Server will quite naturally increase. Furthermore, there are fewer access restrictions on a VPS, and the server provider will typically not have the same resource restrictions on a Virtual Private Server than on a shared web host.
So even though a Virtual Private Server is still a “shared environment” in the strictest sense of the word, VPS hosting WILL give greater performance, simply due to the lack of other users on the machine. The only way to increase performance beyond a VPS is to consider transitioning to a true dedicated server, as required. This will ensure 100% access to the resources. The VPS is still a great way to get dramatically increased performance if your website demands it, without paying the substantial extra cost that might be required for a true dedicated server.

There are two types of Virtual Private Server web hosting in common use. Linux Virtual Private Servers will run Apache software for web hosting, and Windows Virtual Private Servers will run some form of IIS (Internet Information Services).