One of the story's main themes is the expression of love through sacrifice. The Happy Prince shows great love for the poor people of the town, and it is this love which motivates him to get the little swallow to remove gold leaf and precious stones from his statue and distribute them to those in desperate poverty. In doing so, the Prince is sacrificing the beauty of his statue to help those in direst need.
As for the swallow, he sacrifices his life out of love for The Happy Prince. He knows that if he doesn't leave soon for warmer climes, he'll perish. Yet out of the love he has for the Prince, he selflessly flies all around the town, dispensing gold leaf and precious stones to those who need them most.
There is undoubtedly a marked Christian tinge to this particular theme. Both The Happy Prince and the swallow are recognizably Christ-like figures in that they sacrifice themselves for love. As both a Christian and a trenchant critic of Victorian society, Wilde advocates the selflessness of the swallow and The Happy Prince as an example for his contemporaries to follow.