How did Apple manage to reduce the storage size of iOS 9 to 1GB from 5 GB in iOS 8?

This is due to a new technology called 'App Thinning'

Now this consisted of 3 parts, let's just have an bird's eye view:

App Slicing: iOS apps are developed to run on a variety of devices, so they come with code to support all them, whether or not your particular device requires it. App Slicing will allow your device to download only those files required by our device. Example: you don't need the 3x iPhone 6 Plus assets if you're running a 4-inch model.

On-Demand Resources (ODRs): It works on the idea that an app probably doesn't need its entire library of resources at any given time, so parts of it can be downloaded or deleted as needed. Developers will be able to specify what code is needed at what times by tagging sections of code as ODRs. These portions will be automatically downloaded from the App Store when they are required and deleted when they won't be needed again.

Bitcode: It refers to an "intermediate representation" of an app that developers will upload to the App Store rather than a pre-compiled binary. This works hand-in-hand with App Slicing, allowing the bitcode to be compiled on demand as 32-bit or 64-bit, depending on the downloading device. This will also allow any compiler improvements made by Apple to be implemented automatically, rather than having developers resubmit their apps.