The Inspiration Age is an in-character term for the period when the Inspired are largely active, around the time of the founding of the Æon Society for Gentlemen. This timeframe is largely the focus for the Adventure! game line, thus it is also known out-of-character as the Adventure! Era, or thematically as the Age of Hope.
It's uncertain when the end of the Inspiration Age would be, but by World War II most incidents of supernormal activity have vanished.