The word "hegemon" was originally used in ancient Greece, and derives from the word hegeisthai (meaning "to lead"). An early example of hegemony during ancient Greek history was when Sparta became the hegemon of the Peloponnesian League in the 6th century BC. Later, in 337 BCE, Philip II of Macedon became Hegemon of the League of Corinth, a position he passed on to his son Alexander the Great.
In more recent times, the term has been used in a more abstract sense to describe regional domination by local powers, or domination of the world by a global power. An example of the fits is China's position of domiance in East Asia for most of its history. The Cold War (1945 - 1990) is often seen as a battle for hegemony between the communist east led by the USSR and the capitalist west led by the United States. Both sides were superpowers battling to dominate the arms race and become the supreme world superpower.
Since the end of the Cold War, the term has been used to describe the United States' role as the sole superpower (the hyperpower) in the modern world.
See also: cultural hegemony.
to be written: the idea of "hegemony" in Marxist theory.