Web 2.0 is a woo term apparently coined in 1999 by Darcy DeanNucci and popularized around 2003 by Tim O'Reilly and the O'Reilly Media Conference.
Web 2.0 refers to an interactive model of user-generated content. It also incorporates such vacuous buzzwords and fads as "cloud computing" and "tag clouds" which will probably both be history by the time you read this, and an alarming erosion of and cavalier attitude toward privacy. It contrasts to the early web, in which web pages hosting a one-way repository of information were largely put up by individuals hosted in their own shell accounts - complete with a tilde (~) in the URL, while corporations' web sites were designed by paid professionals.
Web 2.0 has considerably dumbed down discourse making anything longer than 140 characters "tl;dr." Marshall McLuhan may have been right after all: the medium is the message. Web 1.0's function was as a tool to find information which could then be put to use and better locate resources in the real world (i.e. offline); Web 2.0's function is to supplant the real world and be an end in itself.
What it means in practical terms is that corporations like Amazon.com and Facebook don't have to pay anyone to create most of their content; instead, you, the sucker with too much time on your hands create it for them. You don't even get paid for it. These corporations then add insult to injury by allowing anyone to comment on what you wrote - which tends to bring out the worst sort of anonymous sniping and character assassination - and by using the content you generated to accumulate buttloads of personal information about your interests and target you with specific advertising. Wikipedia, being a non-profit, works on the same model sans the targeted advertising, instead soliciting donations from its users - so not only are you writing their content without getting paid for it, but you are paying them for the privilege of your labor being exploited in this way.
Hmm. What am I doing writing this here, then?