What gesture is triggered by wiggling your finger on the home button? I've noticed that if I wiggle my finger in an upwards and downwards direction on the home button on my iPhone 6S running iOS 9 half of the screen slides down; as shown here:



I can't find any documentation of what this is or any use for it (tapping the space just closes it, dragging it down pulls down the control centre). It's accessible from any app. 

Would love to know what it is!
You're triggering "reachability" by double tapping a Touch ID enabled home button on iPhone 6 and later. It's designed to allow you to more easily reach the top of the screen when using a larger iPhone one-handed. 

http://www.tekrevue.com/tip/reachability-iphone-6/