A thresher is a person or machine that separates grain from the plants by beating (Oxford Dictionary). While the threshing machine pictured above was steam-powered, mules were used to transport it from location to location since motorized vehicles were still a new concept at the time.
(Photo with description taken from “Haubstadt Centennial Booklet: 1955 Echoes of the Past”, page 39. This book can be found at the Fort Branch Public Library.)