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In general, over-sampling is a technique of collecting data points at a greater resolution (usually by a power of two) than the final data resolution should be. These data points are then combined (down-sampled) to the desired resolution, often just by a simple average. The combined data points usually lack aliasing artifacts or moiré patterns.
Full Screen Anti-Aliasing by over-sampling usually means that each full frame is rendered at double (2x) or quadruple (4x) the display resoultion, and then down-sampled to match the display resolution. So a 4x FSAA would render four over-sampled pixels for each single pixel of each frame.
More often than not, FSAA is implemented in hardware in such a way that a graphical application is unaware the images are being over-sampled and then down-sampled before being displayed.