This is Minecraft Dragons Mod 1.7.9 which adds dragons into your game. Dragons can fly when ridden on and can be tamed, but you must train it. If you ride it too much without success, it will start attacking you, but if it does this, you can still attempt to tame it. Once tamed, dragons will not despawn, and you can fly them around.
All credits goes to the creators of this cool mod: thehippomaster and SpaceInvaders