Psychoanalysis was a school of psychology that arose around 1895, when Viennese physician Sigmund Freud co-authored a book, Studies in Hysteria, with Josef Breuer, a fellow physician. This book documented the puzzling case of Anna O. (real name Bertha Pflugenheim), a young woman suffering from conversion hysteria, a disorder in which physical symptoms occur for no physiological reason. At times Anna would become paralysed, unable to speak, blind, numb in her hand, and so on. Freud reasoned that because there was no organic cause, the symptoms must be caused by psychological factors — the mind. Freud thus became the first to propose that the mind itself could be sick. (It was already known that the brain could be sick.)
This ushered in the era of the "Medical Model" of psychopathology — the notion that maladaptive behaviors should be seen as illnesses. Because illness is not usually seen as something under your control, mental illness removed responsibility for actions and is the basis for the insanity defense in a criminal trial.
Freud came to believe that Anna's strong repressed feelings of hostility toward her hated father gave rise to the troubling symptoms. He found that he could alleviate her symptoms by un-repressing these feelings and making them conscious. Thus was born "the Doctrine of the Unconscious" — the notion that psychological disorders were based on repressed feelings hidden from consciousness.
In addition, Freud came to see almost all of human behavior as directed by unconscious motivations. The little mistakes that we make every day — slips of the tongue, forgetting birthdays, not being able to recall a friend's name, and so on — were not just accidents but were directed by the unconscious. When a would-be Romeo asks the well-endowed woman in a tight sweater to step outside for a "breast of fresh air", it is the unconscious peeking through in a "Freudian slip." Freud's book, The Psychopathology of Everyday Life inventories these kinds of "accidents."
This doctrine of the unconscious was part of "psychic determinism" — the notion that all behavior was the result of unconscious impulses. But to treat a patient Freud had to first ferret out the unconscious causes so he could make them conscious. Psychic determinism allowed Freud to discover the unconscious urges and impulses through "free association" — having the patient talk about whatever came into their mind. Psychic determinism assured that whatever came out of the patient's mouth was important to their problem.
Freud also found that when he asked patients to free-associate, they often began by relating a dream full of revealing symbols. Because of this, Freud called dreams "the royal road to the unconscious" and eventually wrote a book called, The Interpretion of Dreams.
Freud developed a theory of personality that served as a framework for his psychoanalytic treatment. He saw personality traits as a result of psychic energy being "fixated" at certain stages of development because of excessive gratification or deprivation. The stages people went through were the oral state, the anal stage, the phallic stage, and the adult stage. Each stage was associated with charactistic traits. For example the oral stage was associated with stimulation of the mouth — talking, kissing, smoking, and so on. The anal stage was associated with stinginess and perfectionism — being a "tight ass" so to speak. Whenever the psychic energy became "fixated" in a stage, the individual expressed the associated personality traits of that stage. Even today we talk about a person compulsively neat, accurate, or conscientious as being an "anal personality." It comes from Freud.
Freud called his theory "psychoanalysis" and for a long time it was the only widely practiced therapy available for psychological disorders. Even today, "psychoanalyse" is used by some as the generic term for any psychological treatment. ( I can't tell you the number of dates I've been on where the young woman would ask me as a psychology major to "psychoanalyse" her. My response was always "Well, first let's get you out of those hot ole clothes. . .")
Psychoanalysis, although never seen as very scientific because of its unverfiable interpretations, did share with Behaviorism an emphasis on determinism (the unconscious). Furthermore, unlike humanistic psychologies, it saw human behavior as mostly irrational.
Freud has often been accused of belonging to the unholy trinity of science. First Copernicus robbed us of our place at the center of the universe, then Darwin denied us special creation, and then to top it off, Freud came along and said we had no free will. Some people attribute the high rate of depression today as the legacy of these three giants. In fact, humanism is seen in part to have been spawned as an rebuttal to these human degrading philosophies. People don't like to believe that we're not special in this universe and don't have free will.
Psychoanalysis is not very well accepted today in most academic circles. Even in clinical practice it's out of vogue — too expensive and of questionable effectiveness. Nevertheless, by introducing "the talking cure," it provided a model for all current verbal psychotherpies, and the sometimes implausible aspects of the theory allowed later competing theories to promote themselves by attacking the "straw man" of psychoanalysis.