The Oedipus Complex is a Freudian term named after a Greek myth in which a man kills his father and unknowingly sleeps with his mother.

Freud described how as a young child, a boy develops an unconscious infatuation towards his mother, whilst at the same time fearing his father and viewing him as a rival. None of this usually happens at a conscious level. It results in an unconscious conflict because the boy desires the love of his mother yet fears the consequences from his father -the unconscious mind at such an age lacks the wisdom to truly understand the situation.

Often, the unconscious will find a satisfactory way of dealing with this conflict. However, in many cases, the solution is far from perfect. The consequences are many fold and may include: a boy who becomes an over competitive man (wants really to beat his father), a man who finds it hard to combine love and sex, a man who wants his wife to mother him etc.

Women experience a similar conflict called the Electra Complex (during the time of formation they often dream of being pursued by a witch (their mother). An unresolved complex has similar consequences to those described for a man. Women will often seek out a man who treats them similar to their father, or who even shares similar physical characteristics. Sometimes, they will do exactly the opposite.

A leading UK hypnotherapist estimates that 75% of the population need to resolve their complex, and that 50% of all heart attacks are caused by these complexes.

It should be noted that many therapists dismiss such Freudian therapies these days. Indeed, many of Freud's theories have been found to be incorrect or outdated now. However, equally true is that he made a huge contribution to the development of psychotherapy and that some of his theories were very precise.
My experience is that the Oedipus and Electra complexes do very much exist and that a major benefit is reaped by resolving them.