To understand this story it is vital to remember that Nadine Gordimer is an author who is South African and much of her fiction explores the various trials and tribulations that her own nation has experienced. Until the 1990s, South Africa was ruled under a system called apartheid, the legal separation of races. Anyone who was not white experienced sanctioned and legal discrimination and were forced to live in "townships" away from where whites lived. Blacks needed "passbooks" to travel through the country. Although this cruel and unjust system ended in 1991, much suspicion remains in South Africa as a result.
However, what this story does focus on is the kind of exacerbated fear that whites suffered in such an environment. Note how the couple invests in a series of increasingly elaborate security devices to protect themselves from racial strife. However, nothing seems to ever be enough to give them the peace of mind they crave:
But every week there were more reports of intrusion: in broad daylight and the dead of night, in the early hours of the morning, and even in the lovely summer twilight--a certain family was at dinner while the bedrooms were being ransacked upstairs.
Thus the family purchase the final measure, the "Dragon's Teeth" for "total security." However, as the story ends, the parents have to hack out their own bleeding and wounded son from the teeth, suggesting that ironically, the protective devices we purchase can harm the very things they are supposed to protect. This story, therefore, provides an incredibly ironic commentary on apartheid, suggesting that the fear that lies at the root of this inhumane policy is driving us to actually hurt and maim ourselves.