Flashmobs have been around for a few years now; I seem to recall hearing about these around the late 1990s or maybe just a couple years later. They were first organized through sites like Craigslist and other city forums and note-posting bulletin boards. Today they can reach even more people through tools like Facebook.
First things first: a flashmob is a coordinated scheduling of a high number of people to appear at one location. Sometimes it's just as simple as "everyone show up at the park at noon" and sometimes they're an action involved, such as "show up at noon and dance in a conga line for 5 minutes". While these flashmobs have generally been pretty benign (except for the one time a U.S. bank robber used something like a flashmob to blend in with a bunch of painters after a robbery), they do present logistical challenges for security. Most of these events have been for artistic or humorous reasons, but it should be part of your security plan on how to deal with these kinds of flashmob events -- especially if what you are protecting is a recognizable landmark or public or even semi-public area.
To get a sense of the power of these flashmobs, check out this report on CNN of how a flashmob essentially shut down a big London train station for 15 minutes as the flashmobbers listened to their MP3 players and danced -- just like in a similar TV commercial which was the inspiration for the event.