AR means Augmented Reality. If your device is compatible with this feature, you will be able to take pictures of your favourite Dragon in a real-world environment and share it in your social networks. You can access this feature from the Dragon selection menu, the picture icon in the top left of your screen. From that screen you will be able to choose between taking a normal picture of your dragon or using the AR mode.
Why can't I see AR mode in my device?
As the AR technology we are using is still extremely new, there are many mobile manufacturers that have yet to implement support for this within their devices. Unfortunately, if the AR option doesn't seem to be available in your game, chances are that your device brand does not yet support this technology. Keep an eye on official updates to your device software and keep checking!