The shapes of small characters are reproduced more faithfully. The smaller size of text that can be read easily is smaller when anti-aliasing is used. In general, you will see documents as they were designed instead of hopelessly distorted by aliasing. And all these advantages are even more pronounced for kanji and other complicated scripts. Better graphics shapes.
Curves are smoother and free of jaggies.
Differences in line thickness of a small fraction of a pixel that are impossible to describe in aliased graphics become easily visible. Better positioning of shapes. This capability makes a big difference in the spacing of Roman text, which improves to the point of being as good as in printed text. Greater information density. You can browse full pages on the small screen of your palm top PC and get a better feel for what they say and how they say it.