Éminence grise, French for gray eminence, is the "true power behind the throne," i.e., a person who influences politics from behind, without being elected or appointed to a public office (or without having inhereted one in feudal societies).
The expression comes from the time of Cardinal Richelieu, who was the visible power in France of his era (more powerful than even the King of France).
The proper way to address a Cardinal is Your Eminence. Cardinals wear red robes, so Cardinal Richelieu was also known as "éminence rouge" (red eminence).
No matter how powerful Cardinal Richelieu may have been outwardly, he, as any good Catholic, regularly went to confession. His confessor was the Capuchin friar Père Joseph (i.e., Father Joseph). It was Père Joseph who had the power to forgive Cardinal Richelieu's sins. It was also Père Joseph whom Cardinal Richelieu consulted before making any important political decision. Indeed, it was Père Joseph who truly controlled Cardinal Richelieu and was, therefore, the true power in France.
Now, today Capuchins wear brown habits (religious garb). But at the time of Père Joseph they were still wearing gray habits. Hence, Père Joseph was known as the gray eminence, and that nickname stuck along for centuries to describe the true power behind power.