iOS 8 wasn't kind to users of 8GB an 16GB iPhones and iPads. Its over-the-air updates required multiple gigabytes of free space, and installing it reduced the amount of free space available on your device. It brought with it the iPhone 6 Plus, which introduced a new "3x" asset size that made apps even larger than they already were. Luckily, iOS 9 should help.
Apple already talked in the keynote about how it had reduced the amount of space required the iOS 9 OTA update from around 4.6GB to 1.3GB, but a more transformative technology only got a passing mention: App Thinning. In short, apps in iOS 9 will leave your phone or tablet with more free space in the first place.
There are three different mechanisms that developers can use to make these apps smaller. The first, App Slicing, is the most significant. Each iOS app binary you download contains a whole bunch of code for a whole bunch of devices—assuming it's an up-to-date, universal iOS app that supports the iPhone 6 Plus and runs on 32-bit and 64-bit devices, the app contains assets for literally every supported iOS device whether your device needs all that code or not.