Cloud services are used to store things such as documents online. This means no hard drive space on your computer is taken up because it is all stores on a cloud based server.
Many websites offer a cloud service. One of these is Google Drive. Where you can save your data online and access it through any computer with an internet connection by simply signing in.
This feature is also offered by Microsoft, where you can make Word or PowerPoint presentations and share them. I see this becoming quite useful in the future as you could do your work on the cloud and sharing it with your teachers which means you dont have to waste paper.
Microsoft also offers this through Xbox Live as you can save up to 512MB of data on it. This means you can download save data for your game and your account.
Other Cloud Services include Dropbox, DotCloud. All these services potentially offer the same service so it is just a matter of choice.