The murder of Clytemnestra by her son Orestes is unique in Greek mythology in that it is the one story for which we have extant versions by all three of the great tragic poets. Consequently, it is insightful to notice how each tragedy privileges different parts of the story. In "Choephoroe" ("The Libation Bearers") by Aeschylus, the middle part of his "Orestia" trilogy, Orestes is obedient to the gods in avenging the death of his father and the pivotal scene is the confrontation between mother and son when Clytemnestra begs for her life. In "Electra" by Euripides the title character has to persuade Orestes to go through with the deed and the dramatic confrontation is now between mother and daughter. In the Sophocles version of "Electra" the emphasis is on the psychological dimensions of the situation; after all, it is from this play that Freud developed his concept of the Electra complex.
Towards that end Sophocles creates a character, Chrysothemis, another sister to both Orestes and Electra. The situation is that Orestes is assumed to be dead and the issues is whether the obligation to avenge the death of Agamemnon now falls to his daughters. There is an attendant irony here in that Clytemnestra justified the murder of her husband in part because of his sacrifice of their oldest daughter Iphigenia before sailing off to the Trojan War (the curse on the House of Atreus, which involves Aegisthus on his own accord and not simply as Clytemnestra's lover, is important but clearly secondary). The creation of Chrysothemis allows for Sophocles to write a dialogue that covers both sides of the dispute. Electra argues that the daughters must assume the burden and avenge their father while Chrysothemis takes the counter position.
Sophocles does come up with several significant twists on the Aeschylus version. For one thing, Sophocles reverses the order of the two murders and has Clytemnestra slain first, which sets up an interesting scene when Aegisthus gets to revel over what he believes to be the corpse of Orestes and makes the death of the usurper the final scene of the play. This becomes part of the most significant difference between the Sophocles version and the others. Whereas Orestes emerges from the skene distraught after the murder of his mother in "Cheophoroe" and is repentant in the Euripides version of "Electra," Sophocles has Orestes calmly declaring that all in the house is well.
Electra is not as central a character to the drama as she is in the Euripides version, mainly because she does not have a functional purpose in this tragedy. Her main purpose is to lament over the death of the father and the supposed death of her brother. She does not provide Orestes with a sense of resolve because in this version he does not consult the oracles to learn whether or not he should kill his mother but rather how he can do the deed. Still, the part of Electra has enormous potential for performance. Ironically, this "Electra" is the least interesting of the three, despite the fact Freud made it infamous: by his standards the Euripides play speaks more to the desire of a daughter to see her mother dead, but since Sophocles wrote "Oedipus the King" it probably seemed fair to point to his version of this tale as well.