When I was little, when the buttercups would bloom in the springtime, we would hold one of them under our chin and have someone else look to see if our skin turned yellow next to the bloom. If it did, that meant we liked butter. It always did, and we do like butter. Very much.
How does a buttercup reflect its yellow color while it is being held within the shadow under a person’s chin?
Shadows are not ‘things’. They are a light deficit relative to the rest of the scene. Other than the light which is ‘casting’ it, a shadow contains all of the (same) light as does the rest of the scene. (If there were no light at all in shadows, you wouldn’t be able to see anything in them.) There is plenty of light under ones chin that can reflect off of a buttercup and carry with it the color of that flower onto your skin.
Which brings me to the next point: shadows are not gray. They carry the tint of whatever is lighting them. This is commonly the sky (blue) but can be anything that is nearby such as foliage (green). In addition, within concave areas (the indent between flower petals, or the curvature where and object meets the ground) the thing casting the shadow will usually bounce light onto itself thereby boosting its own color.
Which brings me to the third point: not only are shadows not gray, they are more often than not, more, not less, saturated than the non-shaded parts of an object. This may be because shadows are usually lit by bounce light which almost always carries a tint, while the primary light is generally more nearly white. It is also because of the self-bouncing already mentioned, and can be because of translucency such as with flower petals. Where light is passing through the flower into the shadow, carrying the flower’s own color, it strongly boosts saturation.
To investigate this for yourself, open any of your own photographs, in Photoshop set the Info palette to show HSB colors and then drag your cursor over lit and shadowed areas of a uniformly (approximately) colored object. Watch the S (Saturation) readout in Info.
Now that you understand that the main cast shadows that you see in a picture contain all of the light in a scene other than that of the primary light, you will not be surprised when I tell you that shadows are themselves full of shadows. Whether or not you can see them depends on the strength of the primary light relative to the many secondary light sources (bounce, as well as light-emitting sources).
Overlapping shadows cast by different objects but caused by the same (single) light source are not darker where they overlap. You can only block the same light source one time. However, overlapping shadows cast either from the same object or different objects and caused by two different light sources will be darker where they overlap. Where they don’t overlap, the light from one source is being blocked; where they do overlap, the light from two lights is being blocked. It’s very easy to observe this in your own home — where you have multiple light sources of nearly the same brightness.