Web 2.0
n. A second phase in the evolution of the web where developers use new technologies to create websites that look and act like desktop programs and encourage collaboration and communication between users.
So what makes a startup part of the Web 2.0 club? It usually involves the company employing at least one of the following technologies or concepts:

• Tagging: The seemingly simple idea of categorizing content has found a passionate following on the Web. Proponents say having people label content online is the best way to organize information; because it takes advantage of the collective wisdom of everyone online.

• RSS: It's been likened to an online paperboy. Short for Really Simple Syndication, the technology allows users to have their favorite sites send content directly to them. Most blogs and news sites offer RSS feeds of their latest content. Feeds can be delivered to a personal Web page or accessed directly from a computer desktop with Web access. The technology has also fueled interest in audio content that has come to be called podcasting.

• Mashups: Google has been a leader in this trend of remixing the Web. The company has taken its most popular services and made freely available the basic technology behind them — application-program interfaces, or APIs. Tinkering with open APIs has become a popular pastime among tech geeks.

• Web services: With broadband connections linking people to the Web as soon as they turn on their computer, the thinking goes that applications like word processing shouldn't be stuck on desktops. Support for the idea has grown since Microsoft announced in November a strategy shift toward Internet-based services. Online-only versions of Windows and Office are on the way.
—Aman Batheja, “Web 2.0 mania revives dot-com investing,” The Seattle TImes, December 19, 2005
The concept of "Web 2.0" began with a conference brainstorming session between O'Reilly and MediaLive International. Dale Dougherty, web pioneer and O'Reilly VP, noted that far from having "crashed", the web was more important than ever, with exciting new applications and sites popping up with surprising regularity. What's more, the companies that had survived the collapse seemed to have some things in common. Could it be that the dot-com collapse marked some kind of turning point for the web, such that a call to action such as "Web 2.0" might make sense? We agreed that it did, and so the Web 2.0 Conference was born.
—Tim O'Reilly, “What is Web 2.0?,” O'Reilly Media, September 30, 2005
2004 (earliest)
MediaLive International, Inc. and O'Reilly Media, Inc. today jointly announced Web 2.0 Conference, a new event that brings together the leading Internet industry figures and companies to discuss and debate the most important issues and strategies driving the Internet economy. The invitation-only conference will focus on the most innovative Internet business and technology developments by industry leaders and influencers spanning the technology, Internet and service industries. Web 2.0 Conference will take place October 5-7, 2004, at Hotel Nikko in San Francisco.

The theme for the 2004 Web 2.0 Conference is "The Web as Platform," reflecting the emergence of the Internet as a platform by extending applications across the Web, enabling a new generation of services and business opportunities.
—“Top Internet Industry Leaders Assemble at Web 2.0 Conference to Drive Innovation in the Internet Economy,” Business Wire, May 03, 2004
Web 2.0 is one of those terms that resists definition, either because the concept is too amorphous, too pie-in-the-sky to have any real meaning, or because the underlying phenomenon is so huge and important that it will burst the shackles of any attempt to pin it down.

However, the term is everywhere these days, so any language site worth its electrons has to acknowledge its existence and at least attempt a definition. The one above is provisional and may change as Web 2.0 changes.

If my definition is too earnest for your tastes, the definition proposed by Greg Knaus in the Devil's Dictionary 2.0 should provide the proper balance:
The name given to the social and technical sophistication and maturity that mark the— Oh, screw it. Money! Money money money! Money! The money’s back! Ha ha! Money!