This is a form of therapy that has its roots in psychoanalytic theory. Unlike psychoanalysis, in which the patient meets with the psychoanalyst multiple times a week for a number of years, psychodynamic psychotherapy usually occurs once a week. The therapist in psychodynamic therapy is also more active than the traditional psychoanalyst who sat behind the patient on the couch. This is a talking therapy, where past history and current motivations and actions are discussed and examined.
The relationship between the person and the therapist also becomes grist for the mill. How the person in therapy feels about the therapist (transference) and how the therapist feels about their patient (counter-transference) become useful tools for looking at relationships outside of the therapy.
Unlike cognitive-behavioral therapy that has a here-and-now approach, often with an emphasis on problem solving and behavior modifying strategies, psychodynamic psychotherapy effects change through bringing unconscious desires and motivations into the light where they can be examined, interpreted, and challenged, if necessary.
While not studied extensively in bipolar disorder, it does have quite a good track record with unipolar depression, it is widely used as an adjunctive treatment, and is what most people think of when seeing a psychologist or other therapist.