Web 2.0 is a metaphor used to describe a dramatic transformation that is occurring on the World Wide Web.
In the development of a software application, the most dramatic changes in the application often occur when going from version 1 to version 2. That's how the "2" signifies great change.
But of course "Web" is not a software application, so the expression is a metaphor for great change.
What is the great change? It is the change from the web as a place where one passively seeks information provided by "authoritative" sources, to one where each person is an authority and offers information or shares creative works. Yedda.com is a perfect example of a Web 2.0 web site.
Part of the revolution of Web 2.0 is its accessibility. Amazon.com was a pioneer in pushing the idea of the value of user-created content when they launched user reviews early on.
I could contribute to Amazon's web site by writing user reviews, but it would be way too expensive for me to create my own web site where I invited content creation by others. In the era of Web 2.0, everyone can create their own web site, based on their own vision, and invite participation of others. Open source (free) platforms such as Drupal and Wordpress have given these tools to the masses.