Dropbox has a really nice video overview of how it works on their page. So far I'm very impressed. I work as an IT consultant and am very familiar with change management systems. Such systems allow developers to work on files together and keep in sync with the same version. Such systems also allow you to see what has changed, restore previous versions etc.
To me dropbox seems like a nice wrapper on an opensource change management system (SVN or the like).
Lifehacker recently reviewed a bunch of filesharing applications but this was the one which really appealed most to me with it's mix of Syncing, versioning and sharing. I love that I'll be able to so easily email people huge attachments now with just a URL (that does not require them to have an account to download). At the same time I'll be able to keep files in sync with friends and customers on different platforms (important for me on the mac).