I've read all of the responses and all of them are wrong. Anyone mentioning that the cloud allows you to access "apps" from an internet connection etc... well, before the cloud, that's what web apps do. And the reason why the shift was made from windows/desktop applications to hosted, web applications.
The cloud is simple. It's autonomous of hardware, regardless of what software it runs. Thus a CPU or a hard drive can kak, or an entire server for that matter, it shouldn't affect the cloud because the cloud is spread across several servers. Compared to a VPS that is hosted on 1 physical server. Even though you can run multiple VPS on 1 server and reduce your overall server hardware requirements, this isn't cloud.
That being said, I can understand why people are confused to what the cloud actually is. Any web app you've ever used is (according to you guys) "the cloud", but I'm saying it's more related to the technology/hardware and the term comes from there. Your web app running on the cloud = awesomeness.