With 3D Touch, the screen monitors the pressure of your touch to allow you to 'Peek' into apps for previewing content and then 'Pop' those that you want to fully open.
You can use this multi-touch feature to peek into emails, pictures, websites and more to quickly view items on your phone. For info on tapping and holding an app to delete it, refer to the Uninstall Apps directions.
The steps below don't apply to the iPhone 5s / 5 / 5c or the iPhone 4s / 4.
Touch and lightly hold an app that you want to preview (email, contacts, etc.).
While holding, view the list of actions that can be taken.
For some apps, when you tap and hold, a Quick Actions menu appears (e.g., 'Take Selfie' and 'Record Video' appear in the Quick Actions menu for the camera app).
You can also peek into items within an app to see a preview of it (e.g., when in email, touch lightly to peek at its contents).
When finishing previewing your content, release the touch screen.
If you want to open an item you have peeked at, press deeper on the phone's screen.
For more info on 3D Touch settings, refer to this support page.