Cloud computing is a general term for anything that involves delivering hosted services over the Internet. These services are broadly divided into three categories: Infrastructure-as-a-Service (IaaS), Platform-as-a-Service (PaaS) and Software-as-a-Service (SaaS). The name cloud computing was inspired by the cloud symbol that's often used to represent the Internet in flowcharts and diagrams.
A cloud can be private or public. A public cloud sells services to anyone on the Internet.
A private cloud is a proprietary network or a data center that supplies hosted services to a limited number of people.
Watch this Youtube Video for better understanding..
http://www.youtube.com/watch?v=ae_DKNwK_ms
Benefits of Cloud Computing
http://www.onthenetoffice.com/blog/2011/01/the-advent-of-cloud-computing/