In ancient Rome, a genius was a personal spirit, similar to a guardian angel. "Genie," in a bottle, has the same derivation. Families had similar guardian spirits, as did cities. After the Roman Republic fell, the idea changed.
The first Roman Emperor was given the honorific title "Augustus" as a recognition of his powerful guardian "genius." It became custom to drink to the "genio augusti" at every meal. The geniuses of other powerful leaders, such as military commanders, were similarly honored.
Nietzsche has a fantastic definition. He wrote, "Great men, like great epochs, are explosive material in whom tremendous energy has been accumulated; their prerequisite has always been, historically and physiologically, that a protracted assembling, accumulating, economizing and preserving has preceded them – that there has been no explosion for a long time." Nietzsche seems to be applying the process at arriving at an epiphany (insight, "aha!" or eureka moment) to historical change.
The definition today revolves around IQ. There are even attempts, however silly, to attribute certain IQs to leaders in the past; Julius Caesar apparently had an IQ in the 150s. Even a small dose of common sense reveals how stupid our fixation on IQ is: imagine measuring athletes' muscle fibers and awarding the one with the most fast-twitch muscle the Olympic gold medal in the 100 meter dash.
David Hume wrote that the way that society treats geniuses is a mirror image of the way it treats the ignorant. Shouldn't we be more careful about whom we call a genius, and why?