We see and hear the term "Web 2.0" being used (and misused) so often these days. Web 2.0 is used to describe everything from next-generation of software services to a bullxxxx generator :)  To answer the question of "What is Web 2.0?", Tim O'Reilly, who introduced the term, wrote up an excellent article on the subject. Below is my summary of this article.

I think the most fundamental concept behind Web 2.0 is the notion of "harnessing the collective intelligence". This means that Web 2.0 services get better as more people use them. This is sometimes known as the network effects, where the usefulness of the service increases exponentially rather than linearly as the number of users increase. To enable harnessing collective intelligence, Web 2.0 apps are built on the architecture of participation. A simple example is eBay. Once eBay was successful in building a critical mass of buyers and sellers, it automatically drew more and more buyers and sellers. This is network effect.

Another fundamental notion of Web 2.0 is that "data is the next Intel Inside". The observation here is that all successful Web 2.0 services are backed by specialized database, from Google's web crawl to Amazon.com's database of products and community to Wikipedia's knowledge base. This makes sense from a business point of view, because specialized database serves as a long-term sustainable strength of these services.

Other aspects of Web 2.0, such as the "Long Tail", the "perpetual beta", and rich user experience, are also interesting traits of Web 2.0 apps.