A trauma team was a group of medical personnel who dealt with patients who had suffered traumatic physical injuries.
In 2365, Doctor Katherine Pulaski reported that her trauma teams were being run ragged in their attempts to treat everyone who was injured. (TNG: "Contagion")
In 2367, Dr. Beverly Crusher told a trauma team to stand by to receive five injured Talarian cadets who suffered from radiation burns and respiratory distress. (TNG: "Suddenly Human")