There are two factors here. One is the relative brightness the other is how directional the light is. Normally, light comes from multiple sources or is highly reflected. In this case, shadows are soft or non-existent because light hits where the shadow is from other directions than the one that is blocked.

Harsh light is generally very bright and very directional. The intensity of the light means that the dynamic range (the difference between the brightest and darkest part of the image) of the camera is going to require more light to be present in the shadow area to get a good exposure (since it can't overexpose the bright part). Compounding that, since the harsh light is very directional, it casts a harder shadow with less light being reflected or diffused to fill the shadow from other angles.

This is why you often see professional photographers using diffusers and reflective umbrellas with their flashes and using multiple flashes that are off camera in order to spread the light out and make sure light reaches the areas that would otherwise be dark shadows from a point light source (an intense light emitted from one point in space).