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Cloud services solve two main problems for iPad users
1: It allows your iPad to store data outside of your iPad which means you have more room for apps, documents, videos and so on.
2: When you save work in the cloud you can pretty seamlessly switch devices and locations and pick up where you left off. This is a bonus when you are working on tasks that cross between home and school.
iOS supports numerous cloud services bit there are essentially a big three that you will find most compatible with a large selection of apps.
Dropbox: These guys innovated cloud storage and are supported on numerous apps and also other devices.
Apple iCloud: Personally I find iCloud an expensive and clumsy solution that receives next to no support out of the Apple Eco system. It does however play nice on most of their devices and apps.
Google Drive: Google Drive is versatile and well supported by a number of apps and devices. Definitely a good option for schools that use Google Apps for Education.