There is a lot of disagreement about what Web 2.0 actually is. Tim O'Reilly, who coined the term 'Web 2.0', gives the following 'compact definition':
"Web 2.0 is the business revolution in the computer industry caused by the move to the internet as platform, and an attempt to understand the rules for success on that new platform. Chief among those rules is this: Build applications that harness network effects to get better the more people use them. (This is what I've elsewhere called "harnessing collective intelligence.")"
The main Web 2.0 websites that people talk about are focused on user-generated content. People often draw a comparison between Web 2.0 and the early internet ('Web 1.0') where websites primarily allowed passive interaction.
To summarise, with a Web 1.0 website, web developers create content and web users view that content; with a Web 2.0 website, web developers work on the technology of the website and web users create the content.
Web 2.0 websites not only allow users to generate content on websites, but they can also interact and collaborate with other users (resulting in the "collective intelligence" that O'Reilly talks about).
People sometimes refer to Web 2.0 technologies as "new media" technologies. However, new media is actually a broader term, which includes all types of electronic communication made possible through the computer technology, including email, internet telephony and streaming video.