It is a way to get rid of jagged edges. In a video game, if you have a straight edge that is diagonal, you will usually see a stair case like line. To get rid of this, anti aliasing renders the image at a higher resolution than you are running the game at (say you play at 800x600, 2x anti aliasing will render the scene at 1600x800 and then sample pieces of that scene to show you).
With text, what it does it blur the edges of the text when you are using a large font. If you have a black "A" on a white background w/o antialiasing then you will only see the A as black, and the background as white. If you put anti aliasing on, then the A will be black, but around it, there will be shades of grey to smooth out the jaggies.
I am pretty sure this is an accurate definition of anti aliasing, but I have been know to be very wrong on these kinds of thing, so someone correct me if they see fit.
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