Hegemony is what Italian sociologist Antonio Gramsci (see picture) termed: "moral and intellectual leadership."  A constellation of many ideas that represented interests of a dominant group presented as interests of all.  Hegemony is also a Greek word meaning leadership and rule. 

In the early 1900s, hegemony was a term used by Marxists during a democratic revolution meaning political leader of the working class.  Gramsci expanded this concept, developing an analysis of how the ruling capitalists class establishes and maintains its control.  Gramsci learned that the ruling class' cultural values were tied to folklore, popular culture and religion, and also that there is no single dominant class, but rather, a shifting and unstable alliance of different social classes.

Power is a related term to hegemony.  Power being the ability to control others, and hegemony meaning dominance through persuasion. 

Hegemony is based on a power structure. In the structure, A powerful group leads lesser groups not through coercion, but through cultural production and therefore persuasion. 

Hegemony is the success of dominant classes in presenting their definition of reality - their view of the world - in a way that it is accepted by minor classes as the truth or common sense.