Web2.0 is also known as cloud computing, and I think that's a pretty apt image of what it is. In my head, I picture a giant cloud of information hovering above me, and that cloud contains all of the applications and information that I'm accessing on my computer. Of course, the information isn't actually floating over me, it's stored on a remote server, but the idea is the same: I can't see where my data is being stored. It used to be that my data was stored on the hard drive of my computer, but now it's stored on the web and I access it through the internet.
A great Web2.0 tool I just learned about is called Delicious. Delicious is a place for you to save links to various websites, much as we use the "bookmarks" tab in Firefox or "favorites" in Internet Explorer. However, because Delicious is Web2.0, those links are saved on the internet, not on your computer, so you have access to them on any computer that you use.
Also, you have the opportunity to create stacks, which are collections of different links all dealing with the same theme. You can organize these stacks, add descriptions of the links and images to represent them, and then publish them so that other people can browse the collection you've put together.
Here's an example of a stack about legos.
And another about comedy shows in Japan.
Although the advantages to saving your bookmarks remotely so that you can access them from anywhere are obvious, I think the stack feature could be especially useful for education. If students are working on a research project together, they could share links to useful websites they found about their topic. You could also have them create a stack about any theme you wished and publish it on the internet. If you're teaching them how to conduct successful Google searches (kind of like a scavenger hunt on the internet), the students could collect their findings in their Delicious account. Also, Delicious has a great feature where you can tag your links with key words, so it's easier to find all of the useful sites for a particular topic.