The precious things mentioned in the story are the leaden heart of the happy prince and the dead bird. They are precious because both the happy prince and the swallow were very kind, generous and selfless. The prince could not bear to see the ugliness, misery and suffering in his city and so gave away all his precious stones and gold to make his people happy.
Similarly the swallow sacrificed his trip to Egypt and acted as the prince’s messenger carrying the precious stones and gold to the needy spreading happiness around. When the prince was blind he still loved him so much that he never left him even though it kept getting colder and colder with winter approaching. Finally when he could no longer bear the cold he died at the feet of the statue and the statue loved him so much that its leaden heart broke into two.
That is why when God asked one of the angels to bring him the two precious things in the garden the angel took the leaden heart and the dead bird and God said that in his garden of Paradise the little bird shall sing for ever more and in the city of gold the Happy Prince shall