Well web 2.0 is a term that has been wildly used for over 2 years now to signify the evolution of the web since the boom era of the late 90's. Its mainly concerned with user participation and user generated content in addition to social networking..etc. O'Reilly was the first to use this term in 2004.
This is a mind map by O'Reilly explaining what web 2.0 is:
As for Web 3.0, more of a continuation of the web 2.0 concept, where people are expecting what the next evolution of the web will be focused on, some say its mobile but most experts talk about the Semantic web where computers will be able to link the web together bringing more context into user web actions. Where for example, your meeting is delayed, you log that in your calendar web app, then its linked to your travel arrangement and other meetings...etc. So "it" knows what other apps you are using and links actions together. Some talk about using natural language for search..etc.
More info go to:
http://en.wikipedia.org/wiki/Web_2.0
http://en.wikipedia.org/wiki/Web_3.0
