Hospital privileges are the right of a physician to use the facilities and equipment of a hospital. Not all physician employees of a hospital have hospital privileges, as they can be removed by order of the Chief of Medicine or the disciplinary board. Hospital privileges are usually specified for each physician employee, so that a surgeon would have the ability to book an operating room, but an internist would not.
A physician does not have to be a hospital employee to get hospital privileges. For example, an independent surgeon may have the ability to book OR space for their patients. As another example, a family practice physician may get hospital privileges to visit their patients when they are in the hospital.
In order to get privileges, most physicians have to have their credentials fully reviewed to determine if they are properly licensed and have the appropriate experience to perform the procedures they are planning to perform.
One of the reasons many procedures are performed in clinics instead of hospitals is the difficulty of physicians in doing certain procedures in a hospital. For example, most abortions are performed in clinics because most OB/GYN practitioners do not want the controversy of performing elective abortions as part of their hospital practice, and many hospitals discourage the practice.
In Pilot, House has his hospital privileges suspended for failure to do his clinic duty, meaning he had no power to order procedures on patients.
In 5 to 9, Cuddy finds out that the on-call physician doesn't have privileges and asks her nurse to call someone who does.