The graphics card is the component used to display images to your monitor. It is used more than just for games. Without the graphics card, there is no output to your monitor. Back in the old days, we used to call these things "video cards", which made it more obvious as to what these things do.
Now different graphics cards have different capabilities. Some graphics cards, as an example, cannot support games that uses DirectX8 and above. Some graphics cards support multiple monitors; others do not. Some graphics cards can do full-scene antialiasing; others do not. The capabilities of the different cards can vary; and how well they do it also varies.