The penumbra is the area where light is partially blocked, creating a gradual transition between the fully shadowed area (umbra) and the fully lit area. You can think of it as the softness around cast shadows and the darkening before form shadows at the terminator edge. The penumbra gets softer the larger the light source is. A softer light source also creates a softer penumbra. In cast shadows, the penumbra gets softer the further the shadow is projected.