First we need to think about the nature of light. When all visible wavelengths of light reach our eyes, we see white. When only certain wavelengths reach us, we see the corresponding colors. When no visible wavelengths strike our eyes we see black.
Looking For Light
For most of the day the sun radiates all visible wavelengths of light, and it appears white. When the sunlight reaches a cloud some of it is reflected away from the earth. The light which passes through the cloud gets scattered by tiny cloud droplets in all directions more or less equally.
This scattering is something like a pinball being bounced off the pins and bumpers; when the light from the sun hits small particles in the atmosphere, it's knocked around. Since the sunlight is scattered fairly evenly by the cloud, allowing all wavelengths to reach us, the cloud looks white.
Growing Clouds
As a cloud grows larger and taller more light is reflected from it, and less light is able to penetrate it. When a cloud gets a little over 3,000 feet thick very little light is able to pass through it, and the base of it looks dark.
At the same time the water droplets at the base of the cloud get larger, and as they do they absorb more light than they reflect. Now even less light gets through the cloud and it appears almost black. These large, light-absorbing droplets often get heavy enough to fall from the cloud as rain.
Just from casual observation we know that these dark, ominous clouds often bring rain. Now we know why they look so dark.