“The dominance of a culturally diverse society by the ruling class who shape the culture of that society—the beliefs and explanations, perceptions, values, and mores—so that the worldview of the ruling class becomes the accepted cultural norm.” (source)
“Gramsci realized that in order to create and maintain a new society, you also needed to create and maintain a new consciousness. The repository of consciousness is culture….
You may be able to seize a factory or storm a palace, but unless this material power is backed up by a culture that reinforces the notion that what you are doing is good and beautiful and just and possible, then any gains on the economic, military, and political fronts are likely to be short-lived.”
Shifting CH means being ‘counter-hegemonic’, acting in both ‘symbolic’ and ‘institutional’ struggles.
Also see the evolution of this concept in the context of complexity theory here.