Cloud is a term that is used to reference a Computer server somewhere in Cyberspace.
There are two kinds of clouds although there can be an overlap between the two types.
 Cloud storage
Cloud storage means that the server is being used to provide Internet based file storage for your private or public use. This storage is generally provided as a paid service but some small amount is provided for free. It can be used for extra storage, syncing information between devices, and as a way to share files between users. It may also be used as a backup for data on your local machine in case of a failure of your local computer.
The main advantage for the user is access to data from anywhere there is Internet access. The user can download an eBook, for example, whenever they wish. This may also provide a way to sync bookmarks, notes, etc. between two or more devices so that you can begin a book at home and then continue it later while riding mass transit to work.
Another use is to provide access for others by telling them the URL to find the data you are sharing. Many users find the cloud is a good way to transfer data between their home computer and their wireless tablet or eBook reader.
 Cloud computing
Cloud computing is a new name for one of the oldest ways in which a computer can be used. It basically uses your local machine for a terminal display device while doing the actual computing on a server. There are many variations of this use where varying amount of computation is done either locally or remotely. Remote servers require an Internet connection to access the remote server so the unit will only work when online. Chrome OS depends on cloud computing.
Sometimes there is a local app used to provide access to the server. The app is typically only a display program. An example is a mapping service on a smartphone where the maps are on a server and the app provides access and communication. Routing and other computational tasks are done by the remote computer. In other cases a more generalized app such as a Web Browser is used to provide the interface. Sometimes data can be downloaded for use offline.