The term cloud computing refers to using the internet and internet based sites to perform computing tasks. An example you are already familiar with is Google Docs. As opposed to using a programs like MS Word or Pages, you use Google Docs to do your word processing, spreadsheets, and presentations. The benefits are easy to see; access to your documents from any computer and the ability to easily share and collaborate with others.
Think about the way you use your computer each day. How much time are you spending doing tasks using your internet browser compared to programs in your hard drive? Many of the programs that you typically install on your computer are now available in a web-based version. Even computers are moving towards a more interent centered set-up. Best Buy and Amazon will soon be selling computers with Google's Chrome OS. These computers, called Chromebooks, will do nothing but access the internet. Interesting idea, isn't it?