Leveling up in the game is the way to unlock more features, advance in the story, and receive rewards! Earn XP by completing Quests, delivering Board Orders or Helicopter Orders, etc. to fill up the XP meter found at the upper left corner of the screen.
Once you level up, not only will you get rewards and unlock features, but all of your Dragons' Stamina will also recharge instantly! Think of it as a way the Dragons celebrate you reaching another level!