Why do clouds appear black?

Heavy clouds have condensed to the point of large droplet formation, failing the Rayleigh criterion for visible light and so no longer scatter them. It is a case of absorption being higher than reflection/scattering that causes clouds to look dark.

Clouds scatter light by a process called Mie Scattering, meaning all wavelengths are scattered equally, so clouds are always white unless the light source itself is missing some wavelengths (e.g. at sunset, when only the red/yellow end of the spectrum hits). However, depending on where you are relative to the cloud and how thick with water droplets the cloud is, it can block sunlight, so rather than a change of colour it is in fact a lack of brightness that you are seeing.

It's worth checking out the summary section of this page for further information. You may also notice that sometimes there are dark clouds and light clouds in the same sky, but if you look at the direction of sunlight you'll usually see that the dark clouds are merely in the shadow of other clouds.