This is the traditional self-healing cutting mat preferred by stencil cutters in Japan. It is soft, pliant, offering minimal resist to the cutting blade, helping to reduce fatigue on your part. With care, it will give you years of service.
 
The mat is placed under the stencil paper to help facilitate sharp, clean lines when cutting a stencil. The mat allows your blade to pierce the paper and at the same time protect your table top. The mat should be a bit resilient and should not contribute to the dulling of the knife, nor should it deflect you blade as you work. 
 
In Okinawa, dried blocks of toufu were used. On the mainland, older-style professional carvers will use a mat of wood. Contemporary studio artists use this self-healing mat designed specifically for this purpose.