Their are many facets to the psychodynamic approach but the main ideas are that human behavior is driven from forces within the mind. In Freud's belief, unconscious forces are what drive human behavior. Freud said this unconscious was crucial in understanding humans. There are three main parts of the brain that are in continual conflict that drive this behavior: the id (your basic urges), your superego (part of your brain that tries to repress your id and moderate/ temper impulses) and your ego (what is ultimately done).
The ultimate drives were sexual and for survival (freud was influenced by Darwin). In other words, many of our unconscious urges were to mate and were repressed which could cause psychic conflict and would lead to many conditions that Freud viewed as problematic. Therapy would consist of trying to uncover these unconscious urges that were "repressed" through processes of free association. Dreams were also thought of as gateways into the unconscious.
Developmentally Freud believed most behavior was set at age 5, and that were stages where some psycho-sexual task needed to be completed (such as weaning, potty training). All of these focused on erogenous zones (pleasure zones).
Psychodynamic theory was considered less scientific espeically when in contrast to the behavioral view (which focuses on external behavior and does not conceptualize anything with the mind). Freud's theories are interesting and inspirational but his methods weren't always scientific. His sample was generally upper class viennese women and a lot of his ideas cannot be tested.