In the simplest terms, cloud computing means storing and accessing data and programs over the Internet instead of your computer's hard drive. The cloud is just a metaphor for the Internet.
Cloud computing is a synonym for distributed computing over a network and means the ability to run a program on many connected computers at the same time. With cloud technology, we are able to store data on the cloud (the internet) and access it from any computing device, use web mail services, web apps etc. For it to be considered "cloud computing," you need to access your data or your programs over the Internet, or at the very least, have that data synchronized with other information over the Net. In a big business, you may know all there is to know about what's on the other side of the connection; as an individual user, you may never have any idea what kind of massive data-processing is happening on the other end. The end result is the same: with an online connection, cloud computing can be done anywhere, anytime.
Cloud Storage
We can use cloud storage and backup services such as Dropbox, Google Drive, Sugarsync, Box, Skydrive etc. to backup or store our data, without the need to have a pyhsical storage device. It has the advantage of mobility, accesibility, cost efficiency, space efficiency and a lot of other advantages.
Cloud Gaming
Cloud gaming, also called gaming on demand, is a type of online gaming that allows direct and on-demand streaming of games onto computers, consoles and mobile devices, similar to video on demand, in which the actual game is stored on the operator's or game company's server and is streamed directly to computers accessing the server. This allows access to games without the need of a console and largely makes the capability of the user's computer unimportant, as the server is the system that is running the processing needs. The controls and button presses from the user are transmitted directly to the server, where they are recorded, and the server then sends back the game's response to the input controls. Companies that use this type of cloud gaming include Gaikai, OnLive and Big Fish Games.
Users can play games without downloading or installing the actual game. Game content isn't stored on the user's hard drive and evertyhing occurs primarily at the server side, so the subscriber can use a less powerful computer to play the game than the game would normally require, since the server does all performance-intensive operations.