Defining "the cloud" or "cloud hosting" can be a difficult because of the wide variety of manners in which it's used by service providers and technology vendors.  Because it's really an evolution of hosting solutions that have existe for a decade, one of the best ways to understand what the cloud is, is to compare it to other similar technology solutions from which it evolved: shared hosting and VPS (or virtual servers).  

The following two articles from myhosting.com do an excellent job of drawing those comparisions, and drilling into the key elements of clound computing. 

Beyond the Cloud Hype

Cloud: the most abused word in hosting