The penumbra is a part of a shadow cast by an object. As seen from the penumbra, part of the perimeter of the light source is obscured, and part of the light source is visible.

For an object to cast a penumbral shadow, the light source must be larger than a point - obviously, since a point cannot be partly obscured, it is either visible or it is not.

Assuming your monitor is a light source: Hold a small pad of paper between your eye and your monitor so that it covers your view of the right half the monitor. Your eye is now in the penumbral shadow of the paper.

The penumbra of the moon on the Earth is the area where a partial solar eclpise can be seen. The penumbra of the Earth on the moon causes a partial lunar eclipse.

The penumbra totally encloses the umbra and the antumbra - i.e. when the light source is larger than a point, any path from outside the shadow to either the umbra or the antumbra must pass through the penumbra.