According to Wikipedia - Web 2.0 refers to a perceived second generation of web-based communities and hosted services — such as social-networking sites, wikis, and folksonomies — which aim to facilitate creativity, collaboration, and sharing between users. The term gained currency following the first O'Reilly Media Web 2.0 conference in 2004. Although the term suggests a new version of the World Wide Web, it does not refer to an update to any technical specifications, but to changes in the ways software developers and end-users use the web.
The way I understand it is that Web 2.0 is just the new way people are using the web. Before you use to go online to just read about news, hobbies, or play games in other words you were a passive reader. Now, you go online to have discussions on topics you are an expert on, to voice your opinion, to meet other people in your field, in others words to collaborate with others all over the world. It's all about collaboration which in turn enables learning. You can call it user generated content aka read/write web, that is Web 2.0.
Originally the web (Web 1.0) was driven by organizations which pushed the content they thought the users were interested in. Now the web (Web 2.0) is driven by individuals who create their content based on their needs and allow others to contribute to it. Users now learn from each other more than ever, which is called peer to peer learning.
Another important part of Web 2.0 is tagging. Before the organizations had to rely on meta tags for their online content to be searchable and ranked higher by search engines. Even though you still should be doing the above as part of SEO, now users have the ability to associate your content with a descriptive keyword or term enabling keyword based classification and search of information which is called tagging. This increases the relevance and popularity of your content which in turn increases the changes of your content being ranked higher by search engines thus found quicker by users.
That is Web 2.0, but then again this is my interpretation. What is yours?
You can find a list and description of the most used Web 2.0 tools at eelearning.