The concept of Web 2.0 was first presented at a conference of the same name organized by O'Reilly. (Tim O'Reilly credits Dale Dougherty, a VP at the company, with coining the name).
The original Web 2.0 conference was held in October 2004 to talk about the state of Internet companies in the post-bubble world. Following the conference, Tim O'Reilly wrote an article called "What is Web 2.0" and the name stuck.