"Drummer" is just an old-fashioned slang term for a modern traveling salesman. In the 19th century, a drummer was a small-goods seller who traveled by train or in a horse-drawn wagon with suitcases of merchandise. There had always been peddlers who traveled hawking their own wares, but drummers were the first wave of what were then called "commercial travelers." They traveled to isolated areas, drumming up sales for various brands.
Here are a couple of links I found online with more detailed information: