With respect to black people in particular, that may not be too much of a surprise, based on existing lower levels of trust in the US medical care system: http://www.phillytrib.com/news/mistrust-of-health-care-system-runs-deep-among-blacks/article_fe34e876-da2a-57f1-a5a7-cb3aa7316e65.html
However, more generally, familiarity with ethnic-related habits that are health-related (e.g. diet and activities) may help a physician make recommendations that the patient will understand better. This does not require being of the same ethnicity as the patient, but it is more likely that a physician of the same ethnicity as the patient will have such familiarity. Gender may also be relevant – a same gender physician may be more likely to have personal experience with gender-related/specific medical issues as the patient.
Patient aspects not related to ethnicity or gender may also be relevant. For example, a patient who plays a lot of sports may find a primary care physician with an interest in sports medicine to be desirable.