A little over a week and it's official. I love 3D Touch. It takes a bit to get used to and into your "muscle memory" but if you train yourself to always use 3D Touch for app launching and peek/pop you will find yourself doing it just like double clicking the home button. It becomes natural.
One of the subset options of 3D Touch is the ability to invoke the app switcher. The App Switcher is typically accessed by double pressing the home button. With the introduction of 3D Touch you can now use the App Switcher by 3D Touching on the middle, left side of the iPhone screen. This works when you're either on the homescreen or have an app open. I'll stick to my opinion that Apple is in the process of "training" owners of iPhones to prepare for life without a physical home button.
There are two results from using 3D Touch to invoke the App Switcher. The first allows you to quickly switch apps by 3D Touching on the spot indicated by the call out above and in one fluid motion flick the screen to the right. This will quickly open the next app. The second result from using 3D Touch for the App Switcher is bringing up the App Selector itself. Once you apply the 3D Touch in the "special spot" you slowly pull to the right and reveal the open apps (as seen in the GIF above).
As I said it takes a bit to get used to. Once you get the hang of it you will find it's much easier and quicker to switch apps while in other apps by invoking this 3D Touch feature. Instead of double pressing the home button you can quickly just flick between apps using 3D Touch.