What is a Virtual Private Server? 
A Virtual Private Server is a mix between a dedicated server and a shared hosting account. With a Virtual Private Server you still share system resources like the CPU and memory with other users but the file system is setup in such a way that you cannot tell the system has anyone else on it; it acts like a dedicated server. The CPU, Memory, and other resources are usually setup in such a way that each person is only allowed to use a certain percent of them so your resources are always available to you. This means that there is not one person, like can happen on a shared system, using all the resources all the time. Since the resources are setup in such a way that each person can only use so much of them, your site will be more consistent because it will always have the same amount of access to the CPU, memory, and most of the time bandwidth.

What is a Virtual Dedicated Server?
Some
Some hosts set up the Virtual Private System different than other hosts. The whole purpose of having a Virtual Private System is that you are more secure than a shared host and you have more control. If everyone on the server has his or her sites served using the same web server then it is not a real Virtual Private System and it is not secure. It is possible to have your file system be virtual so no one else can get at it but if you are sharing the same web server then that all of a sudden makes it so it is not as secure and you should go with a different hosting company because they are only giving you about one quarter of what you really should be getting.

File System
A system of storing files on the hard drive and in this case the files are stored in such a way that only your account(s) have access to them. This is more secure than shared hosting where everyone is on the same file system and could go look in other areas where they should not be.

Root
This is the super user, or the user with control over everything, on a computer system. This user can do anything they want on the computer system from installing software to deleting everything on a system.

Control Panel
A web based interface, which allows users to administer their server by clicking on different icons instead of having to memorize commands. The commands would be run on the command line and if typed in incorrect they could seriously harm a system and stop it from running forcing the hosting company to have to restore the system from a backup.

Command Line
This resembles DOS in that it is just a blank screen with a prompt where the administrator/user would type in commands for the system to run. Most users would rather use a web base interface or a graphical interface to administer their system because there is less chance of error.