when you take a smaller image, and you blow it up larger, it has jagged edges from the pixels... basically all digital pictures are made of tiny squares of color, the pixels, and if you make a small image much larger, then you can see these squares. kinda like if you sit too close to a bigscreen tv before all the HD stuff, it looks grainy. or if you blow up a photograph way beyond what the quality of the negative can make a good print from.
anti-aliasing, in the sense of blowing up pictures, is letting the software which is upsizing your image, try to figure out how to smooth those jagged bits over. If you just blow up an image more than is realistic, it can end up looking either too jagged or too blurry, depending on how much anti-aliasing the software is applying.
and ya, they use it in games too, to smooth over rough pixelated edges and make things look smoother.