A Computer Graphics Card is the part inside your computer that generates the image and then displays it on your monitor. It provides advanced 2D and 3D graphics for complicated tasks like playing the latest 3D games or watching HD Video.
Traditionally the Graphics Card was in the form of a Card, but on most modern Desktop Computers you generally find the Graphics Card build into the motherboard as an on-board graphics chip.
Pictured below: Motherboard with on-board Graphics
The Graphics Card has one or more physical sockets which allow you to plug in a monitor, TV or other display device. It can control the image output for a single monitor or even multiple monitors.
For specialist tasks like playing the latest 3D games you may want to buy a more traditional Graphics Card as these generally provide better performance levels. Manufactures like AMD are now even building Graphics chips directly onto their CPU, s, these are known as APU,s.