Shared Hosting allows multiple customers to share the resources of one computer, so it is a very economical solution to hosting websites. In most cases all websites share the same IP and server hostname. This has several drawbacks already because if the single IP is the target of a DDOS attack, all websites hosted on that IP may go offline until the attack is blocked. Also, should that main IP become blacklisted due to a customer you do not even know sending out spam from the same server you are on, all of your email will be blacklisted.
The Virtual Private Server (VPS) is designed to be economical, by allowing multiple customers to share the resources of one computer, yet with an extremely high degree of privacy and insulation. The separation is achieved by running a complete separate operating system for each customer. VPS customers have "root" level access and can enjoy many of the benefits of a dedicated server, at a much lower cost. Each VPS has its own IP addresses, users, groups, ports, firewall rules, files, libraries, etc. Very little is shared among VPSs besides the overall system resources.
If you lease a 2.4GHZ Server with a dedicated server host, it is very likely that on a daily average, you are using no where near 2.4GHZ. What virtual private servers allow us to do is resell those unused CPU cycles by hosting multiple servers within the same physical hardware. Each VPS has its own set of resource guarantees, always enough to run the OS. Each can burst up to full utilization at any time.
