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What is the algorithm employed by video cards when one talks about for example 8xAA? I thought the algorithm was about looking at neighboring pixels for correction. Yet, I hear that the implementation is just upsampling followed by downsampling.

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There are various algorithms to do anti-aliasing. I think that the one that you mean is called super-sampling. The idea is that the scene is rendered in x8 resolution of what you eventually see. Then it is low-pass filtered, to eliminate aliasing of higher frequencies in the next step, which is down-sampling x8.

This is described in detail here.

There is a more general discussion of AA algorithms here, and another type of AA algorithm called Multisample AA here.

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