A synonym people who want to sound intellectual™ use for “biggest” or most influential.
Originally from Ancient Greek, it was used in the 19th century to denote the global influence of European colonial powers (e.g. Britain as the “global hegemon”). Later adopted by Marx to describe the “cultural hegemony” of the ruling class, i.e. how it brainwashes people outside university to like capitalism. The idea was most infamously fleshed out by Stalin’s little henchman, Antonio Gramsci (Frankfurt School).