'The Eumenides' completes the Oresteia trilogy. The story takes up right where the 'Libation Bearers' ends. Orestes has just killed his mother and fled to the temple of Apollo. He has cleansed himself and Apollo himself reassures him that he will be protected. The Furies (aka Eumenides) have chased him there and being put under a spell from Apollo, promptly fallen asleep.
Unfortunately for Orestes, the ghost of his mother Clytaemnestra has also shown up and she isn't happy.
"You - how can you sleep?
Awake, awake - what use are sleepers now?
I go stripped of honor, thanks to you,
alone, among the dead. And for those I killed
the charges of the dead will never cease, never -
I wander in disgrace, I feel the guilt, I tell you,
withering guilt from all the outraged dead!
But I suffered too, terribly, from dear ones,
and none of my spirits rages to avenge me.
I was slaughtered by his matricidal hand.
See these gashes - Carve then in your heart!
The sleeping rain has eyes that give us light;
we can never see our destiny by day.
She succeeds and wakens them. The search for Orestes to destroy him but before they can do so, they are stopped by Apollo and Athena. Orestes (truthfully) claims that he was given the task of killing Clytaemnestra by the gods and should not suffer. The Furies will have none of it. For a son to kill his mother is an outrage. If he goes unpunished, the law may as well be throw out.
At Athena's urging, they form a jury out of Athenian townspeople. Each side will present their case and the jury will decide if Orestes should be punished or not. Athena herself will break any tie. The jury decides in Orestes' favor and he is spared.
The Furies are, well, furious. They declare that they'll curse the land and be generally vengeful. Athena appeals and appeals to their better nature. Using her skills of reason, she convinces them to stand by the verdict and protect the court and the land.
This is a play about a maturing system of justice. The normal laws of vengence have already wiped out two generations of a twisted family and are now threatening a third one. Each death had some justification but there is no end in sight. Some impersonal agency simply has to step in and decide what justice is. Only once that is done can any kind proper conclusion come to the story. When the Furies buy into the verdict, that system of justice can be in place.
I'll admit that I don't fully follow the Furies ethics. It is awful for a son to kill his mother, but that's simply the latest in a chain of awful acts. Is it more awful than ambushing your husband? Is it more awful than letting the murder of your father go unpunished? It definitely isn't more awful than killing your daughter to get better weather! And yet this is the crime that exercises them.