The story
From back + forty, meaning “back side of a farm”. In the Homestead Acts (1860s–), farmers were granted a quarter section; a section was nominally 1 square mile containing 640 acres, a quarter section was 160 acres, and the quarter section was itself subdivided into four quarter-quarter sections of 40 acres each: two front forty and two back forty. Compare north forty, back of beyond, backcountry, and backwater.
Etymology from Wiktionary, CC BY-SA 4.0.