Electra disappears before the half-way mark in Libation Bearers, never to be seen again. From the standpoint of the plot, she doesn't do very much; even though her encounter with Orestes in the opening scene gives him a boost of encouragement, she couldn't really be said to get the ball rolling – she just keeps it in play. (Orestes has already made up his mind to get revenge before the beginning of the play.) And yet, she has always fascinated readers of the play, from ancient times up to the modern day. It's no coincidence that the other two ancient tragedians whose works survive to the present day – Sophocles and Euripides – each tried their hand at writing a tragedy focusing entirely on Electra. So what's the big deal?
The main reason why people are fascinated by Electra is simply because of her own personal qualities. To begin with, she is fiercely intelligent and strongly attuned to the nuances of social relationships. This sense of nuance comes up, first of all, in her questions about what is the appropriate prayer to make to Agamemnon's spirit on behalf of Clytemnestra. As she astutely realizes, there is no appropriate prayer – except perhaps for the rebellious prayer proposed by the Chorus (we'll get back to that in a minute).
She also shows her acute sense of social relationships when she first addresses Orestes – or rather, when she addresses him as all of the different family members she can no longer rely on. This sense of nuance in social relationships also translates into powerful intuition about genetics and family ties. Even though it seems silly to us, you've got to give Electra credit for being able to figure out that Orestes had visited the tomb – based on the lock of hair and his footprints. Once again, however, a sense of social protocol factors into her assessment: she knows that the only other person who would have been bound by ritual to make an offering to Agamemnon is his wife, but she's his enemy. Thus, by process of elimination, Electra concludes that it has to have been Orestes.
All of these examples show Electra's intelligence. But intelligence isn't Electra's only positive personal quality. She also has a strong sense of courage and dedication. Even though, in coming with the slave women to the tomb of Agamemnon, Electra is fulfilling a social obligation to her mother, the prayer she actually makes at the tomb is profoundly rebellious. Or rather, it represents a shift in loyalties, from her mother to her dead father. This shows that Electra is fearless about doing what she thinks is right.
Electra also sticks to her guns in adhering to her more conservative understanding of gender roles. Unlike her mother, who violated traditional gender norms, Electra prays to her father's spirit to prevent her from engaging in such behavior. We can see a similar traditionalist streak in the way that Electra silently obeys her brother when he tells her to go inside the house and keep quiet while he plans his revenge. Unfortunately for us, Electra's obedience means that we don't get to see any more of her fascinating character for the rest of the play.