What does "region to be shaded" mean in the PCF paper?
Texture mapping is the process of providing a mapping from the surface to a location on the texture. That is, given a particular point on a surface, you can find a specific point in a texture that corresponds to it. Giving positions a UV texture coordinate is a common means of defining a texture mapping, but you can use a function of arbitrary complexity.

Texture mapping is at least theoretically reversible. That is, given a particular texel, you can use the texture mapping to determine where on an object that texel appears. Of course, not every texture mapping is reversible. Some mapping cause a texel to be used in multiple locations on a surface, and not every mapping uses every texel in the texture.

But the important part of the reverse mapping operation is this: a texel maps to some area of the surface, not a single point.

Shadow mapping is a form of texture mapping. It defines a mapping from the scene to a texture by performing perspective projection of the points in the scene onto the surface of a texture, based on a light position.

If you reverse this mapping, a texel in the shadow map maps to an area in the scene. This is the "region in the scene".