The psychoanalyst Sigmund Freud (1856-1939) famously introduced the Oedipal Conflict or Complex, according to which a male child feels rivalry with his father for the affections of his mother (i.e., his father's wife or partner).
The Electra Complex posits a parallel dynamic for female children, according to which a young girl feels rivalry with her mother for the affections of her father (i.e., her mother's wife or partner).
Pop-culture term: "Daddy Issues?"
Significance of Electra Complex: The popularity of Freudian psychology in the early 20th century and the staying power of the Oedipal conflict as a psychological or dramatic dynamic gave the Electra Complex some temporary popularity as a hypothesis. O'Neill in Mourning Becomes Electra adapted it for dramatic purposes.
After the early 20th century, especially as women psychologists gained influence, the Electra Complex became obsolete except in Literature. As the quotation below indicates, the dynamics of the Oedipal conflict are not necessarily applicable to feminine relations within a family, which focus more on shared identity than on conflict.
So today the Electra Complex is an old psychological curiosity that can come to momentary life in some historic literature but doesn't go much further than that.
"Most writings about the Oedipal stage focus largely or exclusively on boys, who are seen to have a particular problem as they start with an attachment to the Mother that they have to relinquish both from the point of view of individual independence and especially as a result of the social incest taboo which forbids excessively-close in-family relationships.
"The Electra complex, identified by Carl Jung [a student & later rival of Freud], occurs where a triangle of mother-father-daughter plays out, is not a part of traditional psychoanalysis. It is neither a direct mirror image of Oedipus, as the start position is female-female connection."