Hegemony is political or cultural dominance or authority over others. The hegemony of the popular kids over the other students means that they determine what is and is not cool.
Hegemony comes from the Greek hegemon "leader." Wealthy lender nations hoping to determine political outcomes and trade decisions have established hegemony over the debtor nations they lend to. As well as the dominance of one group or nation over others, hegemony is also the term for the leading group or nation itself. During the American Revolution, colonists fought to throw off the British hegemony.