Ezinma is one of Okonkwo's daughters and his favorite child. She serves as a contrast to Nwoye, Okonkwo's eldest son, and also demonstrates Igbo cultural attitudes toward women and aspects of Igbo spirituality.
Okonkwo says of his daughter, "She should have been a boy." This shows us that the traits that are admirable in Igbo culture are masculine. Ezinma is the kind of child Okonkwo can be proud of -- except that she is a girl, so he cannot openly praise her or leave her his inheritance. On the other hand, Okonkwo's eldest son and heir, Nwoye, is his polar opposite. He thinks Nwoye is "soft," not a hard-worker, not manly enough. Okonkwo even has a hard time believing Nwoye is really his son. Ezinma's character shows the reader what type of son Okonkwo wants to have, as does the character of Ikemefuna, the captive from a neighboring tribe.
Beyond the interpersonal relationships between Ezinma and other characters, her presence in the novel indicates the sexism or misogyny of Igbo culture. The society, at least in Okonkwo's village, is apparently patriarchal, with men having the leadership roles as well as multiple wives at home. Ezinma is a strong-willed girl who shares her father's interests, so the two of them have a more natural rapport than he has with Nwoye or his other children. However, it is not acceptable for a father to favor his daughter in this village.
Finally, Ezinma's illness and supposed status as an ogbanje shows us about the spiritual beliefs of the community. The ogbanje is thought of as a spirit who keeps returning to the mother's womb (the mother has miscarriages). When one of these spirit children does survive, though, he or she may be at risk and there are procedures that must be followed, rituals to uphold. We see these when Ezinma has to help the priest find a pebble that is associated with her curse, as well as when the priestess comes to take the ill Ezinma to an oracle in the middle of the night with no explanation. After that journey, though, she seems to recover. These incidents give the reader insight into the cultural and spiritual practices of the village.