What exactly do emergency medicine physicians do?

ER docs are. Usually hospital based, fully trained medical school graduates, and generally have done er residency training. This provides them with general knowledge of all obstetric, medical, surgical, and traumatic cases, knowing what tests to order, which consultants to call, and who needs admission, and who can be released once cleared with a follow up plan.
Not enough space. Screen every patient that comes through the er for life/limb threatening conditions regardless of presenting complaint or ability to pay. This includes reading most x-rays, ordering/interpreting lab tests, doing a wide range of procedures, and deciding whether a patient needs admitted. We also consult with other specialists as needed.