What is the moral purpose and cultural significance of the story "The Nighingale"?

The moral of the story is that nature offers more beauty, variety, and power than the manmade, mechanized world. This is illustrated through the beautiful song of the real nightingale.
The nightingale's song is so beautiful that it thrills the Emperor of China and his court, but when the Emperor is presented with a mechanized, jeweled nightingale, he likes that one better because it is more beautiful. However, its song is more repetitive than the real nightingale's: lacking in spontaneity. And worse still, the imitation nightingale breaks.
The real nightingale's song has the power to cure the emperor's disease as he lays at the point of death. In fact, it seems to bring him back from death. The song also has a natural power, and the bird possesses a natural wisdom that a mechanized bird can't replicate.
The story was written in the nineteenth century, which was characterized by a culture that was increasingly driven by material consumption and the idea that joy can be found in man-made items. The story therefore challenges that assumption; it argues that true joy and healing come from the natural world, equally available to the rich and poor alike, as symbolized by the nightingale.

The moral of the story, I would argue, is that nature is always more beautiful than anything artificial. The Emperor, though initially enchanted by the sweet song of the nightingale, eventually loses interest in the little creature, becoming charmed and enraptured instead with a mechanical bird. But this shiny new toy, like all human artifacts, eventually breaks down. Yet what is natural, such as the beautiful song of the nightingale, will always endure.
The nightingale also represents truth as opposed to the falsity of the mechanical bird. When the Emperor listens to the nightingale's song, he's living according to nature, and his fidelity to the truth brings him great joy and happiness even in the midst of serious illness. Yet whatever enjoyment the Emperor derives from the toy bird is fleeting; like the toy itself, it cannot last.
Andersen wrote the story at a time of rapid industrialization in Europe. In this environment, nature was seen as an object, something to be used and exploited for human gain. The Emperor in "The Nightingale" briefly succumbs to the prevailing Western attitude towards nature, before returning to an understanding more at one with the world around us and all its joys and beauties.