Then, all of a sudden, the goddess Athena shows up. She explains that she had business in Troy that she was taking care of. Then she says, "Wait a minute—who are all these weird people hanging out here? Don't worry; I won't judge you before you let me know what's up."
When the Furies reveal their identity, Athena says, "Oh yeah, I know who you guys are."
Then the Furies explain how they are pursuing Orestes because he murdered his mother. Athena doesn't accept this as an answer, however. She wants to know why Orestes killed his mother.
The Furies don't think that's relevant. After some arguing back and forth, Athena finally suggests that they put the matter to a trial.
The Furies are cool with that, so long as they get some respect (they seem to be a little insecure in that department).
Then, Athena turns to Orestes, and asks if he would be willing to put the matter to a trial.
Orestes replies that he has been purified of the crime because he has performed sacrifices. Then he explains how his mom (Clytemnestra) killed his dad (Agamemnon), which is why he (Orestes) killed Clytemnestra.
For good measure, he also mentions how the god Apollo put him up to it. With that out of the way, he says, that, sure: he's up for a trial.
Then Athena says something unexpected. She says that this is too big a deal for her—a goddess—to judge on her own.
Instead, she is going to appoint a jury of mortal Athenians to help her out. This will be the beginning of an institution, responsible for presiding over murder trials, which will last for all time (or so she says).
Then she tells Orestes to go get his witnesses and get his case together, while she rounds up the best citizens of Athens to sit on the jury.