The video card - also known as the graphic card - pretty self explanatorily is in charge of the computer's graphics. It is a lightweight card that plugs into the computer, which displays its graphics capabilities. So the pixles that make up the images on your screen are stored in the video card, and the computer decides what to do with the pixles in order to make the image. The graphics card is what takes the ideas of the computer and brings it forth into a viewable display, whether it be an image, or the words you are reading right now. But in order to take the binary data of the CPU and turn that into a picture you can see, you need a translator. This translation usually takes place in the video card, unless the computer has graphics capability built into the motherboard. (Check this out for more information on the motherboard).
While the elements and ideas behind a video card are simple enough to grasp, the process and excecution is quite difficult. The CPU and the software applications work together to send the information of the image to the graphics card. The pixles on the screen are then formed into an image by the video card and the information is sent back through the monitor. (Here's more about the monitor).
The Graphics vary depending on the adapter, which are available in abundance for whatever your graphics needs or preferances. Some modern computers do not have physical video cards but have GPUs merged with the motherboard. This is a cost effective style of computer, great for who uses a computer for work or at home and does not need or care for advanced graphics. Always remember to pick the video card that's right for you. Depending on the display monitor and the logical circuitry, the look and display of your graphics can range in aesthetic and resolution. There are also multiple video modes, texts, and graphics. In text mode, the monitor can only display ASCII characters. In graphics mode, the monitor can display any bit-mapped image. Nowadays, most video adapters also hold memory so that the RAM is not being used to store displays. (Click here if you want to know what the RAM is actually used for).