Tim O'Reilly's Web 2.0 Overview
"The concept of "Web 2.0" began with a conference brainstorming session between O'Reilly and MediaLive International"

Web 2.0 Principles and Best Practices
An O'Reilly Radar Report
"More than just the latest technology buzzword, it's a transformative force that's propelling companies across all industries towards a new way of doing business characterized by user participation, openness, and network effects. "

Explaining Web 1.0, Web 2.0 & Web 3.0
"All of these sites, like Facebook, use the concept of a social networking to create a community. Each community member is responsible for contributing information to the rest of the users. Even though social networking is the most popular approach, another prominent approach is the development and utilization of web services."

My Explanation :)
In my words Web 2.0 is not a "new" internet. It is taking the standard website that just gives information and turns it into a site that allows the user more interaction, input, collaboration, and communication. To me this is what the internet is all about. As our society becomes more interconnected between websites, cellphones and text messaging the web will have to continue to evolve and adapt to the demands placed on it.