This is a great thing for us in education and the good news is that there are a wide range of educational apps that support AirDrop sharing including: Pages, Notability, Explain Everything, Book Creator, Creative Book Builder, Tellagami, iMovie, Keynote and many more. Now students can, for instance, create screencasts and share it with their peers in the class instantly without requiring any internet connection.
In this wonderful video tutorial EdTech Teacher sheds more light on some other ways you can use AirDrop in combination with some of the apps mentioned above with your students. Enjoy