Basically the idea behind app thinning is that it will exclude data that you don’t need from the download. As it stands, every app you download contains assets for literally every supported iOS device. This is regardless of whether you will need that data, so for example if you’re running an iPhone 4 that can’t take advantage of certain features of an app that is only available for iPhone 5 and above, the app will download all those assets anyway.
This means that your phone is storing a bunch of data that you will never ever need. This is the equivalent of software developers who bundle Windows and Mac softwares together in a single file, just in case you might install it on a Windows or Mac computer. It is redundant. So with iOS 9’s app thinning, the iTunes App Store will be able to work out the data that you need and delivery it accordingly.
This means that apps can be downloaded more quickly and take up as little space as possible without redundancies. As for the developers, they won’t need to do anything on their end as they will keep uploading complete versions of their apps, with the App Store taking care of compiling and sorting it out according to the device.