Black is due to the absence of direct light striking on that region due to blockage by the body whose shadow is formed. 
we can say
A shadow is caused by an object blocking light so that it doesn't reach a surface. The area in shadow appears black because there is no light falling on it so
it appears dark. 

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Shadow is formed when a light incident on an opaque object.So, Shadow is black because no light is reached the surface where it is blocked by that opaque object.