The graphics controller in your computer converts data supplied through the chipset from the CPU to a bitmap image, and it sends that image to a video display monitor. Modern video controllers are single-purpose computers that offload the burden of creating images from the CPU.
For two-dimensional images, the graphics controller card needs enough RAM to hold two complete bitmap images, plus some extra for overhead. The number of bits in an image is equal to the screen resolution (width times height, in pixels), multiplied by the color depth. 3-D images consume much more RAM because they must include the z-buffer, polygons, and textures.
There are many makes and models of graphics cards, but most of them use chipsets supplied by either NVIDIA or ATI. All video cards with the same chipset and the same amount of RAM have very similar performance. Most of the features that make the difference between a relatively inexpensive graphics controller and a screamingly fast, high-quality 3-D card make little or no difference on anything except cutting-edge games, video editing, and streaming video from the Internet or DVD playback.