Cloud computing describes a new supplement, consumption and delivery model for IT services based on the Internet, and it typically involves the provision of dynamically scalable and often virtualized resources as a service over the Internet.
A more user friendly explanation is offered by Commoncraft: Cloud Computing in Plain English
Here are a few more visual explanations from Youtube:
Cloud Computing Plain and Simple (by rhirschfield)
Cloud Computing Explained (by HighT3chDad)