Anti-aliasing renders the picture at higher resolution to find the fraction of a pixel covered by a polygon. When you read 8x AA that means each pixel is divided into 8 and most calculations are done that many times instead of 1.
Suppose the GPU finds that the object covers the 3 of the points. Then the color values are combined by mixing 37% of the color of the object and 63% of the background. If the object is moving, you might find that it covers 6 samples on the next frame. Now the amount of color imparted by the object is greater. The result is that motion appears smoother because the object doesn’t have to jump by a whole pixel.
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