Why does my screen go down half way when I tap the home screen 2 or 3 times?

It is a feature called Reachability.

Reachability

Reachability helps you more easily interact with items at the top of the screen on iPhone 6, iPhone 6 Plus, iPhone 6s, and iPhone 6s Plus.

Bring items within reach. Go to Settings > General > Accessibility, turn on Reachability, then lightly double-tap the Home button to bring the top of the screen into reach.

See here: https://help.apple.com/iphone/9/#/iph66e10a71cand http://www.imore.com/how-use-iphone-6-and-6-plus-one-handed-reachability

-AJ

Not sure if any of you considered that it’s not supposed to have anything on top? It’s to bring the top of the screen down within the reach of your “one handed” thumb.

That’s why it’s called Reachability - so you can reach the top of the screen with one hand.

There isn’t supposed to be anything up there. This feature is to bring down the top of your screen to reach it more easily while you are holding your phone.

Great. What is it reaching? There is never anything up there...

I agree. There's nothing up there. And it has been driving crazy for a while. So, thanks for telling us not only how to activate it, but how to deactivate it.

It is moving the icons at the top, which you can't reach holding the phone with one hand near the bottom, down a bit so you CAN reach them.

But there is only a cloudy grey area up there for me. I can't activate any icons; nothing happens when I touch the grey area. I can see no benefit at all to this "feature".