AA smoothes out the "jaggies" in an image that occur when lines aren't perfectly vertical or horizontal, resulting in a "stair-step" appearance. AA fills in the gaps and smoothes things out. Fact-paced shooter games don't really need it, but racing games, flight sims or anything that you have time to really stare at benefit greatly. The difference between AA and non-AA visuals in THPS3 was shocking.
I'm sure someone else will post links to somewhere with examples.