Anti-aliasing is a filtering process for digital media files intended to “smooth out” the harsh “digital” look or sound that digital media can have. The reason that digital media (images & sounds) need such filtering is that digital media is not smoothly created; instead, time and picture samples are taken which adds an unnatural sharpness or pixellation to recorded images or sounds. Another way to look at this is to imaging a smooth flowing curve, such as a sine wave. Then, imagine a bar graph with each column reaching up to the curve and touching it. Notice the gaps between the curve and the graph column? That is aliasing at work.
One way to reduce sampling errors is to increase the timebase of the sample. That is why CDs sound better than MP3 files, as the sampling occurs at a higher rate. However, ask an audiophile to compare CDs to vinyl, well, sit down and grab a beer…
Another way to reduce sampling errors is to approximate the values as they transition between the actual digital samples. In an image, this amounts to “blending” the colors/values in between the original pixels. In reality many neighboring pixels are sampled and weighted to get the best possible result. The more you understand anti-aliasing, the better you can control how the filtering can work to meet the look you are going for.
There are several different ways to anti-aliasing rendered imagery, and each has their strengths and weaknesses. Typically, the biggest weakness is the time it takes to generate the anti-aliasing in the first place, as that process typically occurs during render time. Again, a quick study of the different methods will further assist you to get to the look you require.