Dynamic perspective uses the Fire phone's four ultra-low powered infrared cameras and four infrared LEDs along with other sensors and special algorithms to track your phone movements and your head position in real-time and quickly render graphics from the appropriate perspective. Dynamic perspective works even if you cover up two of the cameras (which is likely when holding the phone), and infrared means it will work even if it is dark. The cool thing is that this in effect lets it show you images in a way that looks like 3-D, even though the display is 2-D. Right off the bat, you will see the 3-D effect on the lock screen and wallpaper images.
The phone's sensors allow for controlling the device with gestures. You can tilt your phone backward and forward to scroll through websites or e-book pages, tilt left to bring up a menu, tilt right to bring up shortcuts and information and swivel to bring up notifications and utilities like Flashlight, Settings and Mayday.
The effect of your gestures will often depend upon context. For instance, in the Messaging app, tilting right brings up photo access so that you can attach and send pictures, and in the Amazon Music app, tilting brings up lyrics to whatever is playing. Moving your head or tilting the phone slightly will change the view on the screen to allow you to "peek" around corners and see things from different angles. In the case of the Maps app, peeking will also bring up more information in the form of Yelp links.
All the gesture controls make it easier to use the phone one handed, but you can also swipe the touch screen to do all of these things, if you prefer.
Third-party developers are already working these features into their apps. Aside from the more utilitarian control uses, there are likely some fun possibilities for dynamic perspective in game apps.