There is no easy consensus about how to define what is meant by Web 3.0, but it is generally seen as a reference to the semantic Web. While it is not that much more precise a phrase, the semantic Web refers to technology to make using the Internet better by understanding the meaning of what people are doing, not just the way pages link to each other.
Confused yet? I think part of it has to do with merging artificial intelligence with the Internet. They reference an earlier article from 2006 (here). Good stuff to keep in mind, I guess. Anyone know anything about this?