Cloud computing is basically Internet based computing where you don't really know what's on the other end. Many of the big Internet companies host "Cloud" services which basically are virtual servers that can be expanded to handle your workload transparently.<quoted text>
Every time your machine authenticates, you're saying "hello" to a "cloud"...somewhere or another.
Most Cloud apps are very small client apps, like those on cell phones, that send minimal data back and forth from the Cloud servers which do the majority of the number crunching. Apple Siri is a very good example of that. The vast majority of the work isn't being done on your phone.
There's an inherent problem in the Cloud in that your data can be mined, and you don't know who is using it to do what. You also have a very hard time getting the data back again should you decide to abandon the service.
Cloud computing is about two things, keeping server administration out of the hands of yahoos, and keeping a guaranteed revenue stream with the parent companies rather than yahoo consulting companies or irreplaceable IT administrators. When it comes down to it, it's for companies who are too full of themselves to do their own IT work.