The 3d world maintained by games is expressed in floating point numbers. The screen coordinates, however, are integers. Now, when objects in the world space are mapped to the screen coordinate system (process known as rasterazation) the conversion from floating numbers to integers causes some pixels to end up in the wrong places. Now, there are two solutoins, first is to have more pixels (increasing the resolution) thus making the mapping process more accurate. And second one is to make the mapping process itself more advanced, which is pretty much what FSAA does.