Most of the points are already mentioned.
Anti-Aliasing (AA) smooths out the lines & edges of objects & images, making them much more smoother. However, it uses a LOT of power from your graphics card.
Usually the maximum advised is 8x, more than that will use too much power & not give you much more smoothness compared to 8x (in most cases).
Another example, one guy who had made custom graphics for GTA IV was using AA at 16x, he was getting only about 21-35 FPS, with a i7 950 @ 3.2GHz, 6GB Ram, 1x nVidia GTX480 1536MB (for Graphics processing), 1x nVidia GTX275 1792MB (for Physics processing), & a resolution of 1920x1080 @60hz.
Whereas, without AA, he would've got about (my approximate) 70-150 FPS