I like this video's explanation:
http://www.youtube.com/watch?v=XdBd14rjcs0&feature=related
The short version: Google and Salesforce.com, among others, sell computer space and 'virtualized' application environments that let you run your program on their machines. Like virtual webhosting, but for programs and applications, not just websites. It's a big buzzword now because the big players are really pushing it as a way to make more money off of their infrastructures and unused clock cycles. Salesforce especially, you can kind of blame this most recent version of 'cloud computing' on them and 'Force.com', since they've been very heavily marketing their service using the term cloud computing, and by proxy, the idea of cloud computing itself.