Psychoanalytic psychology is a major paradigm of psychology that attempts to create a conceptual frame work built around psychoanalysis. To a large degree psychoanalysis is still based on the concepts developed my Sigmund Freud in psychodynamics but it also encompasses expansions of the ideas from people like Carl Jung and Alfred Adler.
Psychoanalytic psychology primarily focuses on clinical applications. It attempts to describe a patients problems as deriving from the unconscious. Psychoanalytic psychologist say that often traumas from various stages of development cause the unconscious mind to stagnate at a particular level of development. The goal of therapy is to address these events and allow the patient to overcome these past traumas and gain conscious control over his life.