The penumbra (from the Latin paenes "almost, nearly" and umbra "shadow") is the region in which only a portion of the occulting body is obscuring the light source. An observer in the penumbra experiences a partial eclipse.
An alternative definition is that the penumbra is the region where some or all of the light source is obscured (i.e., the umbra is a subset of the penumbra). A body in the umbra is also in the penumbra (and, I believe, a sould as well...).