Eminence is superior status. If you become a world famous actor, the folks in your home town might treat you as an eminence when you come home for Thanksgiving. Just don't expect your family to do the same.
Eminence traces back to the Latin adjective ēminēntia, meaning high or lofty. We don't usually use it for mountain tops, however; it's social loftiness that scores eminence. Some special people are addressed as "your eminence," in the same way you'd call a judge "your honor." You can attain eminence or be an eminence. If you become a physical therapist, you might work with another kind of eminence: the high bit protruding from a bone where tendons or ligaments attach.