Mastering Shadows By Olivier Saraja

Size of the shadow buffer (BufSi)

As we have seen before, information about pixels that get light or shadow is stored in a buffer, which acts exactly the same as a rendered picture. This means that the shadow buffer has its own resolution, than can be set accordingly to the effects your are after. By default, Blender's buffer size value is 512x512 pixels.
 

BufSI set to 512	Zoom: The shadow is blocky

This kind of effect is good enough when the camera from which the final picture is rendered isn't too close to the shadows, because at a distance, it is very hard to tell about the blocky look of the shadow.
 

BufSi set to 2048	Zoom: The shadow is far more progressive

When you increase the Buffer Size, of course, the shadow gets more accurate borders, better for close shots of an object and its shadow. BufSi behaves exactly as the resolution of a rendered picture does.