What is Eminence ?
Eminence is (noun) (formal.) 1. a high place The castle stands on an eminence overlooking the river. 2. high rank He owed his position of eminence in the government entirely to his friend the Prime Minister. She was met by several persons of great eminence in the university hierarchy. 3. used as a form of address to a cardinal His Eminence, the Cardinal Archbishop of Westminster (NOTE: When speaking directly to a cardinal, say Your Eminence.)
source: Easier English, Student Dictionary Upper Intermediate Level