colonialism (spoilers)
Fausta is an indigenous girl who lives in such poverty that she doesn't even have the means to bury her dead mother. In order to accomplish this, she must work for Aida, a white, wealthy lady (for what is probably peanuts). Although Aida is an artist and in no way a nouveau riche, her large, beautifully decorated house is certainly luxurious compared to anything we see in Fausta's neighborhood.
It is possible that the mistress-servant relationship between Aida and Fausta is to a certain extent a commentary on the relationship between the white and the indigenous people of Latin America from colonial times to the present.
As others have pointed out, Fausta is so desperate for money that she must sell her voice/soul to Aida, much like The Little Mermaid does to the Sea Witch or Faust does to the Devil: she trades her songs of sorrow for pearls, which Aida is very reluctant to give her in the end. (The connection between Aida and the Sea Witch is hinted at through Fausta's song, which is about a mermaid, and the pearls.)
Indeed, Aida is portrayed as a selfish character who ruthlessly takes advantage of Fausta. This is especially evident when she doesn't want to honor the deal they've made (in which they've agreed to trade singing for pearls). Her avarice is also hinted at when Fausta first arrives at the house and is informed that Aida would deduct the cost of the uniform from her salary (something only a tightwad would do, I think). More importantly, she never acknowledges in public that it is Fausta who has provided her with music. Claudia Llosa, the film's writer and director, seems to be condemning the way that indigenous people in Latin America were cheated and oppressed by white colonizers, and how even today, wealthy (predominantly white) people continue to abuse their position of power.
I looked up the symbolic meaning of pearls and found that there are numerous references to them in the New Testament, in which they often represent the wickedness and pride of a people. One example is Revelation 18:16, "And saying, Alas, alas, that great city, that was clothed in fine linen, and purple, and scarlet, and decked with gold, and precious stones, and pearls!" In the film, the pearls represent what is only a small luxury for Aida and yet something that Fausta can initially only dream of obtaining.
Aida and her son don't really communicate with Fausta unless they need something from her (her services or a new song). The son, in particular, completely ignores her. It's as if he and Fausta lived on different planes of existence. I don't think he ever says a word to her or even looks at her in the eye. To me, this may be a way of pointing out that the poor and the wealthy in Latin America often live in different worlds, even when they share the same space. (While in some cases the employees of a household are treated like family, Fausta's and Aida's relationship isn't altogether uncommon.)
There are several references to the past in the movie. Fausta's mother is one example. Not only a victim of colonialism, she has also been forever scarred by the radical leftist guerrilla The Shining Path, which caused a bloodbath in Peru. The songs that she sings describe their brutality and haunt Fausta. The violence of the extreme left is presented as a horrible problem on itself. Another reference to the past is the doll which Aida had buried in the garden hoping that it would disappear forever. Could Aida also have been a victim of The Shining Path? Or could the doll represent the colonialist past, one that is too inconvenient to look back to at this time and age? This isn't addressed very clearly.
Some posters have complained that this movie is an insult to the poor. I feel the opposite: if anything, it might suggest that the soul of the country rests in their hands. Aida, frustrated with her lack of inspiration, throws her expensive piano out the window. But Fausta is able to turn her suffering into music (much like a blues artist might). The gardener has gained wisdom by working the land. Fausta begins to trust him when she sees this in his hands.
That is not to say that the film romanticizes the poor in general, though. A variety of very different characters inhabit the story. The neighbor who courts Fausta is decidedly unsensitive and driven by an animal-like lust. Her uncle has a good heart and wishes to help her but is very primitive. Also kind is the gardener, who has a more sophisticated and grounded understanding of the world around him. Fausta, the heroine, is special, like the rare potato that blooms. Despite the political allegories that one may find in the film, its story is mainly about her spiritual journey to freedom.
In fact, I think that Llosa is more severe in her criticism of the wealthy. While her depiction of Fausta's family and neighbors is very nuanced, Aida is nearly presented as a caricature of evil. She's an interesting villain with flashes of humanity, but there's little to no sympathy for her as a person. Willingly or not, though, she appears to play an important role in helping Fausta with her personal quest.
Whichever the case, the film addresses very real social problems and it does so in a refreshingly poetic and tasteful way.