Web 2.0 basically refers to the transformation of Internet or Web-based applications from static HTML pages to dynamic ones...Social Networking sites like MySpace or totally Geek sites like Digg or bookmarking sites like Del.icio.us or sites like Flickr or YouTube and also applications that can be used online like word processor app Writely or Google Spreadsheets consitute Web 2.0.
Web 2.0's approach is that of people connecting and interacting with each other more frequently.
BTW, Web 2.0 is more, if you can say so, democratized ie more oriented towards Open Source applications than being tied to the proprietary systems...for eg. witness the rise in popularity of Open Source (free) apps like Firefox, OpenOffice, Linux etc.
Although, there's something called Internet 2 also, that refers to the network of computers, limited to academia, govt., military that is more secure than the one we use...it I think uses IP V6 protocol, a much secure protocol for communications.
Hope this helps!