In a play that's definitely got its fair share of strangeness, the title itself might also seem more than slightly odd. Mourning Becomes Electra. Who's Electra? There's not even a character named Electra in the play. Just what is O'Neill doing here?
We know that Electra's the name of the sister of Orestes in Aeschylus's tear-your-heart-out tragedy The Oresteia, and that the play was all about the destruction of a particular family (members of the House of Atreus). So we can bet that we're going to see a play dealing with the same kind of theme, albeit with some important differences. One of these changes—and this is the second signal—is that this play is going to revolve around the story of a strong-willed daughter instead of a son. The name Oresteia basically means that Aeschylus's trilogy is all about Orestes. Using Electra's name tells us that we're going to be following an Electra-type figure. That figure is Lavinia Mannon. So "Electra" in the title of the play actually refers to Lavinia in the play.
Then there's the rest of the title. It's hard to think of mourning "becoming" someone. That turn of phrase "X becomes a person" is a way of saying that something suits them, seems to be doing them good, or looks good on them, as in "that dress really becomes her." While guilt and grief may consume Orin, Lavinia seems to morph into the picture of health and beauty after her parents' deaths, as if the act of mourning has turned her into a beautiful woman. Like she's found a new shade of lipstick that does wonders for her eyes. And yes, that should creep you out.
There's also another way of reading the title. Mourning Becomes Electra can mean that mourning literally becomes Electra (or, in this case, Lavinia, because Lavinia = Electra). It can mean that mourning completely takes her over. But don't just take Shmoop's word for it; let's get it from the horse's mouth. O'Neill said that by using the title Mourning Becomes Electra, he sought to convey that mourning befits Electra; it becomes Electra to mourn; it is her fate; black is becoming to her and it is the color that becomes her destiny. (Source)