So, what is this Web 2.0 thing?

If you are confused about what Web 2.0 really is, don't worry, most everyone is. It is a broad category of web technologies that expand upon or improve upon the way the web used to be (hence being dubbed 2.0).

Wiktionary.com's Web 2.0 definition:

The second generation of the World Wide Web, especially the movement away from static webpages to dynamic and shareable content

Wikipedia's Web 2.0 entry includes:

Web 2.0 concepts have led to the development and evolution of web-based communities, hosted services, and applications; such as social-networking sites, video-sharing sites, wikis, blogs, and folksonomies.

Both Wiktionary and Wikipedia are examples of Web 2.0.

Other common Web 2.0 examples:
eBay
Craigslist
Flickr
iTunes Music Store
MapQuest
Google Maps
Gmail