The old-fashioned method of antialiasing is called super sampling. An image that is 800x600 is upscaled by, for example, 4 times, to make an image that is 1600x1200 inside the graphics processor. Each pixel in the original 800x600 image has its colour altered dependent on the 4 pixels around it in the 1600x1200 image so that when the image is downsized back to 800x600, the edges appear less harsh. Here's an example of how that technique works:
This technique is good, but is a killer to performance – because of the upsizing needed, the performance of the graphics card is significantly reduced because it has to do, effectively, 4 times the work to render the same screen. This was the first anti-aliasing technique to be introduced, back with older cards like the GeForce 4. The primitive method of quadrupling the image size is what accounts for the enormous performance hit that we saw on that generation of cards when enabling anti-aliasing, and almost caused the abandoning of the entire technique. However, luckily for us, a new technique was invented called Multi sampling.
Multi sampling is a slightly more developed and intellectual approach to the problem. Multi sampling was introduced with DirectX 8. Rather than creating a larger, virtual image to calculate the samples, cards that multi-sample take the colour averages from the original image. Additionally, samples are reused for neighbouring pixels, meaning that less calculations have to be done. For instance, if we are sampling two adjacent pixels at a time using 4 samples – imagine the points are one above the other – we only really need 6 samples shared between the 2 points, whereas we need 4 samples each if we calculate them in isolation.
Because the image is not being upsized, the performance hit of anti-aliasing usuing multi-sampling is significantly less.