Crash course to anti-aliasing:
It works to counter aliasing effects on a screen made of pixels.
FSAA (full screen anti-aliasing) affects both polygon edges and textures to reduce aliasing effects, but the most notable effect is on model edges as shown here:

Close-up:

This is what anti-aliasing does. Depending on how it's done, it smooths out the kinks in diagonal edges and reduces the jagged effect that is caused by pixel-based design.
Incidentally, this is the main reason why I would want displays to increase their pixel density and colour depth instead of physical size. 22 inches is plenty sizeable widescreen display; 24 inches is excellent. But if resolution is increased while keeping the display's pixel density constant, it still won't improve things like this, while reducing pixel size and increasing pixel density would result in sharper image, smaller pixels would lead to less apparent jagged edges on same sized display at same view angle, and it would essentially reduce the need for gimmicks like anti-aliasing while making it possible to use higher resolutions.
Pecenipicek, post-processing only disrupts FSAA on times where a model is silhouetted over a light effect such as explosion, engine glow or explosion. Other times it seems to work quite nicely.