3D Touch is a new feature found in iOS 9 on the iPhone 6s and iPhone 6s Plus. It uses Apple's Taptic Engine and pressure sensors to sense the amount of pressure you apply to your display. A light touch, for example, allows you to preview things like emails, photos and even directions in Apple Maps. Users can also apply more pressure to "pop" open emails, Maps and more. You can fine-tune the amount of pressure it takes to perform a "peek and pop" transition by navigating to Settings > General > Accessibility > 3D Touch.
You can disable 3D Touch in Settings > General > Accessibility > 3D Touch.