One of the movements, or phenomena, to come out of Central New York was the birth of numerous religions, new sects of major religions and religious movements. The famous revivalist Charles Grandson Finney who is credited for being the driving force in America's Second Great Awakening described it best, "what was born one day, was burned-over by something new the next day." In reference to the many spiritual wildfires that blazed in Central/Wesern NY. Hence, the "Burned-over District' came to describe this phenomena.
Associate Professor of Philosophy and Religion at Keuka College has put together an informative video on the Burned-over District. It diverges a bit off topic by speaking about the Bluff Point Ruins, and emphasizes the Keuka Lake Region, but it is well done: