Web 2.0, according to Wikipedia (which is itself a Web 2.0 technology), is "a term describing the trend in the use of World Wide Web technology [i.e. the Internet–mhays] and web design that aims to enhance creativity, information sharing, and most notably, collaboration among users." Unlike typical product releases (Blackboard 8.0, for example), Web 2.0 does not refer to a new and improved version of the web. Instead, the term reflects a change in how people and industries are using the web together.
There is considerable disagreement about what, exactly, Web 2.0 encompasses. It is a very ambiguous (perhaps deliberately so) term, so I suppose individuals can interpret Web 2.0 as they see fit. Let’s see if we can come up with our own definition based on some of the primary characteristics of Web 2.0 technology.
First of all, there is one common thread that seems to connect most definitions — using Web 2.0 to enhance the ability for people to communicate with each other. In a previous post on this blog about conversations online, a commenter posted the following:

Not only do conversations matter in Web 2.0, conversations are what define Web 2.0.
Gone are the days when messages get blasted out and picked up by unassuming recipients. We have too many competing messages and we’ve adapted by doing some serious communication filtering.

This idea that Web 2.0 is all about conversation is crucial to understanding the transformation of the web from a relatively passive activity to an extraordinarily vibrant activity. In the olden days of "Web 1.0" technology, people navigated from web page to web page, quietly absorbing information from the web site. If you wanted to comment on a web page, you had to email the web site’s author. Now, almost all Web 2.0 web sites that people visit (blogs, wikis, social networking, social bookmarking, discussion forums, and more) have immediate feedback mechanisms. Furthermore, Web 2.0 tends to focus on the production of "microcontent" instead of "macrocontent".
According to Bryan Alexander, who wrote an article for the March/April 2006 issue of Educause Review, microcontent describes snippets of information such as blog posts, or the streams of conversation/revision involved in creating a wiki page. Content should be reusable and should not be limited to only one form of technology. This idea of reusable content makes it easy to post content in multiple places on the web in different forms in different locations. For instance, we in Educational Technology take pains to make sure that our help files on Blackboard and Respondus are available in both a web-based version and a printer-friendly PDF version. This way, folks can download the PDF files for easy retrieval later or they can access our web site on demand if they need a refresher on parts of the technology in question. We also go the extra step to break down the content into the easily digestible chunks of relevant information (a task-based approach instead of a features-based approach).
So far we have established that Web 2.0 involves conversation and the creation of microcontent.
Conversation, by necessity, requires the participation of two or more people engaged in meaningful (hopefully) dialog. In other words, all parties involved in the conversation participate. It is possible to be an observer simply by browsing and reading, but in order to participate, you have to engage the other parties by responding to what they say or by allowing them to respond to what you have to say. Web 2.0 technologies encourage this participation in the conversation to a remarkable degree.
Another key quality of Web 2.0 technology is that it is always available through a web browser. There are a wide variety of web browsers, each with different capabilities (on campus we support Microsoft’s Internet Explorer, Mozilla’s Firefox, and Apple’s Safari). In other words, the web becomes a platform (much like Windows and Macintosh are both platforms for running applications as well as operating systems) for running web-based applications. We are all familiar with web applications in one form or another (if you have done any online shopping, participated in an online survey, or used Joe’SS/PeopleSoft here on campus you have used a web-based application). A web-based application is a way of offering a particular service through a near-universal mechanism available to all users of the web. There are some instances where a specific browser might be required (I’m looking at you, Microsoft!) and other instances where a specific technology might be required (e.g. Flash plugin), but these technologies are readily available for download from the web if you know where to go. If you don’t know where to go, use a Web 2.0 technology such as Google to find it.
At this point, we have established:

Web 2.0 allows users to engage in conversation, post microcontent, very much encourages active participation of all users, and provides a host of services to users and communities through near-universal web-based applications available to all interested participants.

I think this definition is as good as any. If we get too much more involved in our definition, then we run the risk of turning a simple blog post (Web 2.0) into a book (Web circa 1439 A.D.).
If you want a much more detailed look at the evolution and definition of Web 2.0, Tim O’Reilly (yes, thatTim O’Reilly) has an online article about Web 2.0 (more in terms of business and software engineering than academics).