Psychodynamic psychotherapy is a framework for working with a range of emotional, experiential, and social patterns in human personality and experience. It is a depth psychology, as it assumes human experience has layers, and that not all of them are in view all the time. In order to bring about change, it is not enough to stay on the surface: you need to explore the thoughts, memories, emotions, and motivations that you are ordinarily not aware of, which are influencing your choices and ways of experiencing life. Unconscious experience is an out-of-view but highly influential part of us, like a “blind spot” that we rely on others to help us see. It is also often based on adaptations that we made in the past, without realizing it, in order to cope with difficult situations. The focus of this work includes trying to bring into view the maladaptive patterns in your particular emotional experience, thinking, and relating. An example of this would be to explore the unconscious reasons for repeating unwanted behaviour (like self-sabotage at work, or provoking conflict in relationship, or feeling enslaved to an addiction) that seem to make all your efforts to stop it futile.
Psychodynamic psychotherapy relies on the empathic dialogue and connection between therapist and client as a key activator of personal change. This therapeutic approach identifies deeper causes of psychological symptoms and issues that affect many aspects of your life. Early childhood experience and the legacy of your particular family of origin are regarded as important influences on present-day experience.
A helpful summary of psychodynamic therapy can be found on Wikipedia.