A hammercloth is a large decorative piece of heavy weatherproof fabric, often fringed and richly adorned with embroidery, gemstones, and cloth of gold, placed over and around the seat of the coachman of a carriage or coach.
A hammercloth might display the arms or other emblems of the heritage of the owner of the coach.
One is that a coachman used to carry his tools, including a hammer, with him underneath his seat to perform repairs to a carriage should it break down on the road.
A third is that it is a corruption of "hammock", and that a "hammock-cloth" was a strip of fabric used instead of a wooden seat in days before carriages had springs for shock absorption.
On a carriage with no springs, a hammock provides a much more comfortable ride than a wooden slat, and so "hammock-cloth" may have been the original term.