Graham is right that Web 2.0 started off as a brand invented for an O’Reilly Conference. He says now it means something along the lines of “using the web as an application,” “Ajax,” or “doing things the way they should be done” on the web.
Here’s his take on Ajax:
One ingredient of its meaning is certainly Ajax, which I can still only just bear to use without scare quotes. Basically, what “Ajax” means is “Javascript now works.” And that in turn means that web-based applications can now be made to work much more like desktop ones.As you read this, a whole new generation of software is being written to take advantage of Ajax. There hasn’t been such a wave of new applications since microcomputers first appeared. Even Microsoft sees it, but it’s too late for them to do anything more than leak “internal” documents designed to give the impression they’re on top of this new trend.
Both this link and the previous one come from Semiologic.