As different patients have different states of mind, it is essential for a general dental practitioner to understand their psychology to treat them accordingly.
For a practitioner (general or specialist), the major contribution of psychology knowledge can be in context of therapeutic relationship. There are various aspects to a therapeutic relationship between doctor and patient, which demand careful consideration. Its not just about "being nice" to the patient. The client has several doubts and insecurities regarding treatment which must be acknowledged with empathy. We can say that cognitive and affective regulation is required during therapy. Whether it is about compliance to medications, understanding of disease, managing pain or accommodating the illness in day-to-day activities - psychology is required.
As a psychologist I may add to my colleague that the greatest contribution of psychology to the different health sciences is the understanding of the doctor-patient relationship, the detection and understanding of possible anxieties and fears associated with a medical practice that may be invasive, and empathy towards the patient. Not to talk if the patient is a child! In those cases, you usually hear the most recommended professionals are the ones that can "cope" with the child's fears in a respectful and comprehensive way. I think in most medical practices, professionals must train this sensitive doctor-patient relationship.
In dentology it makes the difference between a dentist concerned with the treatments, ignoring affects-merely a job to be done and done well like a mechanic fixing a car- and one concerned with the patient, easing the patient through often painful and alarming treatments.