The Flies takes place in the town of Argos, Greece, a city plagued by a huge swarm of flies for much of the play. Based on information we gather from the god, Zeus, and the townspeople, it seems that the flies first arrived in Argos fifteen years ago, after the murder of Agamemnon. We have a not-so-subtle hint from Sartre to look further into the text:
The flies? How do the flies come in?
They are a symbol. (1.1.45-6)
A symbol of what? It helps to look at the end of Act II, when, right before Electra's eyes, the flies turn into the furies. In Ancient Greek mythology, the furies were the goddesses of vengeance. If you did something really awful against your own family, like murdering your mother, then the furies would come after you in the name of vengeance. In The Flies, however, the furies are called "The goddesses of remorse." Not the goddesses of vengeance.
This is an important point. If the furies act as the goddesses of vengeance, it suggests that there is some universal system of morality in which killing one's mother is wrong. It further suggests that the perpetrator deserves to be punished because he has violated this system of values. For the existentialist, however, individuals are expected to choose their own value system. The Flies doesn't morally condemn any action, nor hold up any one ideal as "right" in a morally absolute sense. Instead, Sartre is concerned with freedom and choice. Remorse is what happens when an individual lacks the courage of their convictions, when they refuse to recognize the depth of their personal freedom, and when they doubt their ability to choose a value system of their own. Vengeance is externally imposed; remorse is self-inflicted.
It makes sense that the furies in Sartre's play are a self-inflicted curse. Zeus may be able to send them after mortals, but, as Orestes points out in Act III, "It's your weakness gives [the furies] strength" (3.1.56). Electra doesn't have power over them being there, just like she didn't have power over the stone that crashed into the temple steps in Act II. What she does have power over is her own interpretation of these events. How will she let the furies affect her? It works exactly the same way with the flies plaguing Argos in Act I. The citizens choose to interpret these flies as a punishment for their crimes and a reminder of their guilt. The flies have no intrinsic meaning of their own.