Web 2.0 is the business revolution in the computer industry caused by the move to the internet as platform, and an attempt to understand the rules for success on that new platform. Chief among those rules is this: Build applications that harness network effects to get better the more people use them. (This is what I've elsewhere called "harnessing collective intelligence.")
He also cites Eric Schmidt's pithy phrase, "Don't fight the Internet," as emblematic of Web 2.0. In the comments to O'Reilly's post, someone wrote one of the best proto-definitions I have seen so far:
Maybe one day my grandson asks me what Web 2.0 is. I guess I'll say: Web 2.0 was the moment when we stopped using computers and started using the Internet.
By that definition, Web 2.0 is not quite here yet. Computers still get in the way too much.