The story
Coined by Charles Grandison Finney, who in his 1876 book Autobiography of Charles G. Finney referred to a "burnt district" to denote an area in central and western New York State during the Second Great Awakening. He felt that the area had been so heavily evangelized as to have no "fuel" (unconverted population) left over to "burn" (convert).
Etymology from Wiktionary, CC BY-SA 4.0.