Poly cutting boards are plastic boards used under leather punching and cutting tools to protect the blades. They absorb impacts and vibrations, and the softness of their material will protect both the cutting blades and the work surface underneath.
When punching leather, it requires a tool to be placed on top of the leather and then hit with a maul or mallet. This drives the blade through the leather and makes the cut. When the blade passes through the leather, it makes contact with the surface underneath. If this surface is metal or very hard, it can damage the cutting blade and make it dull or ineffective.
Placing a poly board under the leather when punching or cutting allows the blade to enter into the softer plastic. This won’t harm the blades, and the blade generally does not go through the plastic. This protects the work surface underneath.
These are a very common leather working tool to have and are available in a wide variety of shapes, thicknesses, and colors.