There are a lot of great information sources that explore the concept of Web 2.0 and Library 2.0 (L2.0). Both terms have been through some serious verbal washings and duly sanforized to reveal complex terminology and user-centered design.
Plainly put, it’s the rise of the personalized web, populated, maintained, and influenced by you. Maybe that’s too plain? If you want to get a better handle on these two terms and what they mean I would recommend reading the following sites:
What Is Web 2.0 – Design Patterns and Business Models for the Next Generation of Software. By Tim O’Reilly
Community 2.0. By Ellyssa Kroski
Do Libraries Matter? The Rise of Library 2.0 (PDF). By Ken Chad & Paul Miller
Update: check out this article from the June 2006 online issue of Webology titled, "Library 2.0 Theory: Web 2.0 and Its Implications for Libraries."