A computer monitor is the viewing display of a computer. People often get confused and call the monitor the computer. The reason they get mixed up is because the monitor is the unit that people look at and is usually quite big. There are two types of monitors, these are the CRT (Cathode Ray Tube) and the LCD (Liquid Crystal Display). The CRT is the older of these two types and is very chunky unlike the LCD monitors which are very thin.
A computer monitor connects to the computer's video card. The information is sent from the computer, processed by the graphics card and then sent through the cable to the monitor where it becomes visible. The monitor does not store information but only displays what is sent from the computer.
This means a computer can run without a monitor but there would be no point as the user cannot see anything he does.
The CRT monitor connects through the VGA (Video Graphics Array) port on the graphics card while the LCD monitor can connect either through the S-VGA port or the DVI (Digital Video Interface) Port.
A pc monitor is measured in inches. Common screen sizes are 15", 17", 19", 20", and 22". Some screens reach sizes of 40" or more but this is rare. A monitor is measured from one corner diagonally to the other. This gives it's size in inches.
The LCD monitors which are more recent then the CRT monitor are very useful in saving desk space and are usually easier on the eyes. LCD widescreen monitors have also become popular and these stretch further across. The widescreen monitor takes a while to get used to but once you do it feels much better. Not only can you watch movies in full capacity but you can sometimes view two A4 pages at the same time and it is much easier to turn your head sideways then up and down.
See this page on how to choose a monitor to work out what monitor is in your budget and suits your needs.