"In general, psychodynamics is the study of the interrelationship of various parts of the mind, personality, or psyche as they relate to mental, emotional, or motivational forces especially at the unconscious level [Wikipedia, Psychodynamics]." Psychodynamic psychotherapy derives from psychoanalysis, but also differs from traditional or classical psychoanalytic technique.
The commonality is in the focus on conscious and unconscious motivations creating internal conflicts that manifest in symptoms. Symptoms can be somatic, psychological (e.g., anxiety, depression, OCD), behavioural (e.g., compulsions, addictions), or characterological. The therapeutic technique involves face-to-face talk therapy, at a regularly scheduled time and frequency. This is referred to as "the frame" of the therapy. Psychoanalysis occurs multiple times per week while psychodynamic therapy is less frequent, but ideally not less than weekly.
In psychodynamic psychotherapy, the psychotherapist listens for unconscious affect and motivations, links present difficulties to historical relational experiences (transference), and assists the client in replacing old templates with new, healthier ones that have greater flexibility. The therapeutic relationship is an important component of the therapy as the client's expected relationship dynamics (transference) are extinguished through new relational experiences.
This is a very simplistic explanation which does not capture the depth of training involved in practicing psychoanalytic or psychodynamic psychotherapy. Of importance, however, is that the focus is not on symptom control, but on understanding the unconscious conflicts underlying the symptom(s). In resolving the conflicts, symptoms are resolved.
Dr. Marilyn Chotem, R.Psych. #773