The precious things mentioned in the story are the dead bird and the leaden heart of the Prince. These two are precious as they sacrificed their lives to help others in their desperate times. The swallow left his trip to Egypt and worked tirelessly every night to deliver the stones by the Prince in order to help the seamstress, the playwright and the young matchgirl. The Prince also gave up his jewelry, his eyes and gold leaves from his body to help them. Thus they sacrificed to provide for others. Towards the end we even see that God appreciates the angel for his wise decision and he would forever allow the bird to sing in paradise and the Prince to praise him.