"Antique Tools," in the Flooring Products, Tools & Supplies on EBAY forum, begins: "Don't remember who was the collector but seen these on e-bay Collection of Antique Carpet Layers Tools/Turn Of Cent. - ..."
I don't think they stood on the plate but kneeled on it as the one I have is padded. But other than that I think that is how it was used. Then they tacked it down to be taken up later to be cleaned by beating the carpet with a rug beater and maybe scrubbing with brush and water.