The underside of a cloud is usually relatively flat. Warm, moist air rises and cools until, at a particular temperature and altitude, water vapour condenses into tiny droplets. As these droplets grow and scatter sunlight, they create the familiar opaque appearance of a cloud. Under particular combinations of temperature, moisture, and atmospheric motion, however, pockets of condensed air and water droplets can extend downward from the cloud base. Turbulence and air currents within the cloud can organize these features into hanging pouch-like structures. The result is the formation of mammatus clouds, named for their distinctive rounded, pouch-like appearance. The source notes that they are commonly associated with turbulent atmospheric conditions and can occur near thunderstorms.
Mammatus can form in different parts of the world whenever suitable conditions occur. Their visibility, however, depends strongly on illumination. Side-lighting from the Sun can make the hanging structures especially conspicuous, whereas when the Sun is directly above the cloud their shape may be much harder to distinguish.
The original article describes these formations as relatively uncommon and often short-lived, sometimes remaining clearly visible for only minutes.
The photograph reproduced in the post was taken in 2012 by Canadian photographer Michael Johnson. It shows mammatus clouds that appeared following a thunderstorm over Regina, Saskatchewan, Canada.