At a time when the land offices were fully occupied, this phrase came to mean a rushing business.
1882. [The Company] once did a land office business in ore-crushing.Report to the House of Representatives, p. 153. (N.E.D.)
1909. Theatres did no unusual business, but picture shows, which are quickly emptied and filled, reported land office business.N.Y. Evening Post, Oct. 11.