While most clouds form in rising air and have flat bottoms, mammatus clouds have pouch-like protrusions caused by sinking air that hang on their undersides.
Mammatus clouds can only form if the sinking air is cooler than the air around it. The sinking air must also have high water or ice content. Though they are often associated with thunderstorms, the clouds are harmless and usually form in pockets of turbulent air after the worst of a storm has passed.
Taken from my balcony in NW Italy.
