Cloud computing is moving some of your local computer tasks into internet via webservices, such as office application and data storage. One of the classic examples, GoogleApp, there is a set of office applications which are similar with your MS Office. But they are running on their servers instead of running in your local computer.
Those servers are a huge processing tasks. None of single server can handle those kind of jobs. So, normally, cloud computing will run on a cloud platform. The clould platform is using grid computing, therefore, grouping a set of computers to form a cluster. Not many companies are providing this kind of service at this moment. As far as I know, Amazon has their EC2 which I hear the most of people are talking about, and from Rackspace, I have mentioned in my early blog post.
Generally, that is relative new concepts and it is still evolving