The term "Cloud Computing" is open to a certain amount of interpretation, but generally speaking, it refers to a computing environment where most of the computation, file storage, and so forth is not performed on your local computer, but rather some other computer (or bank of computers). With modern cloud computing, most activity is done via a web browser on a PC. The argument can be made that HotMail and products like it were early forms of cloud computing. Now, some very sophisticated applications are available in "the cloud", such as word processing, spreadsheets, database, etc. Some of the advertised advantages of cloud computing are location independence (if you have access ot a browser, you can compute), reduced cost in some situations, and so forth.
Those of us who have been in the computer business for a few decades simply call "Cloud Computing' "Mainframes Redux"