Mike Beasley, writing for 9 to 5 Mac:

A new iOS 9 feature added in beta 1 was only discovered when users attempted to update to beta 2 earlier today. This new feature will allow the operating system to intelligently delete applications if you don’t have enough free space to perform a software update. Once the update is complete, the apps will automatically be reinstalled and your data will remain intact.

Apple is taking this storage space issue very seriously.