Oedipus complex is a term Sigmund Freud introduced. Freud said it was that someone wanted to have a sexual relationship with the parent of the opposite sex, and to kill the parent of the same sex. Freud uses the figure Oedipus, from Greek mythology: Oedipus killed a man in a fight, when he didn't know this man was his father, king Laios of Thebes. In that time, the Sphinx besieged Thebes, and gave riddles to those who passed. Those who weren't able to answer or solve the riddles, would be killed or eaten. Oedipus was able to solve the riddle, and as a prize, he received Iokaste, the widow of king Laios. He didn't know that Iokaste was his mother. The Sphinx was very ashamed that someone had been able to solve the riddle, and killed itself.
Freud developed a whole theory, and he says that humans are driven, which is comomnly known as drive theory ("Triebtheorie" in German). He said that all children between ages three and five have what he called fantasies of incest. He also thought that the opposite case: the love of the same-sex parent, and the rivalry with the opposite-sex parent was normal.