Cloud computing refers to applications and data that don't reside locally on your PC, but on a host computer administered by someone else and accessible via the Internet. Gmail, Flickr, and Yahoo! Mail, for example, are all are on the cloud. On the one hand, you can access your work from anywhere; on the other, you're dependent on a remote system to maintain it.
For general overviews of cloud computing, NPR ran a story in August 2008, and InformationWeek has posted a useful Guide to Cloud Computing.
You can read a PDF version of the report "The Tower and the Cloud: Higher Education in the Age of Cloud Computing," at the EDUCAUSE website. Print copies are available for purchase as well.