Psychodynamic psychotherapy is also known as an "insight" approach, because it is the practice of exploring deeply the inner workings of your mind (how your psyche actually works). Old, unresolved conflicts and beliefs drain energy from us; imagine trying to walk when your muscles are ridged and tense, effectively locking you in one place. Over time, it's pretty exhausting and dispiriting.
By using an insight approach, we're intending to understand these stuck places in your psyche so that the stuckness—the inability to move forward in your life—can relax with the awareness of new options. When you really see that now, in your current life, you actually have fresh possibilities for action, the old painful dilemmas naturally melt away.
To make permanent change in the reoccurrence of depression and anxiety, my experience is that insight therapy, in combination with the skill building of CBT and mindfulness training, is essential in creating change that sticks.