3D Touch is a new feature on the iPhone 6s and 6s Plus that gives the touch screen a whole new dimension of functionality. With it, the user can perform a simple tap, a tap with a little bit of pressure, and a tap with even more pressure to bring up the "Peek and Pop" features.
One of the more useful features afforded by 3D Touch is the ability to transform the keyboard (only Apple keyboards, no third party ones yet) into a track pad for easy navigation through what you've written. To activate it, simply press firmly anywhere on the keyboard, then slide your finger around it to move the cursor within the text. Press a little harder and you can drag to highlight the text under the cursor.