There are many different types of setting and different roles in which people can become leaders in the health profession, and the specific skill mix is slightly different in each. Running a department in a small rural hospital and having a role in a large government department responsible for public health require different skills.
First you need a broad, not just a specialist knowledge of the health care field. As a nurse, you might specialize in geriatric or neo-natal care, but as a nursing administrator, you might be supervising nurses in all departments of a hospital. That doesn't mean you need to be able to do everything all your subordinates do, but you need to know enough about their tasks to make good decisions about what sort of administrative procedures and policies will enable everyone to give the best patient care.
Next, you need strong skills in managing people. You also need to know finance and budgeting, and possible marketing as well. You also must be knowledgeable about regulatory issues and good at writing reports, conducting meetings, and managing workflow.