The purpose of Athena's intervention at the end of the trial of Orestes in Aeschylus' "Eumenides", the final play in the "Oresteia" trilogy, is to resolve what appears to be an intractable moral dilemma. This is a role often termed "deus ex machina" or "the god from a machine" because in Greek staging the god who resolved such dilemmas often was lowered onto the stage from above by a mechanical crane.
The particular resolution was the problem of retributive justice, in which Orestes, to avenge his father, becomes ritually polluted by matricide. Athena's argument is if the Furies then just kill Orestes, we get a system of justice in which there is an endless cycle of retribution, and that the only way to end the cycle is not with more blood but with a new system of justice, in which courts replace individual vengeance. Thus the final scene represents a foundation myth for the Court of the Areopagus, in which the Furies become the Eumenides, goddesses who enforce justice through the courts. Athena proclaims their new role in lines 1155 sq.:
To all my citizens I'll act with kindness,
setting in place these goddesses among them—
powerful divinities, implacable—
whose office is to guide all mortals' lives
in everything they do. If there's a man
who's never felt their weight, he's ignorant
of where life's blows arise. His father's crimes
drag him before these goddesses, and there,
for all his boasting, his destruction comes—
dread silent anger crushing him to dust..