Black rain refers to rain contaminated with dark particulates such as soot, ash, or other atmospheric dust. It can occur after events like wildfires, volcanic eruptions, explosions, or nuclear fallout. Most notably, "black rain" describes the radioactive rain that fell after the atomic bombings of Hiroshima and Nagasaki in 1945. This rain contained radioactive materials combined with ash and soot stirred into the atmosphere by the intense fires and explosion. The particles gave the rain a black color and sticky consistency. It fell about 1-2 hours after the atomic bombing, carrying radioactive fallout to the ground. People exposed to this rain faced radiation exposure, which has had lasting health implications for survivors. The black rain was produced by three types of clouds from the bomb: a cloud of soil and dust lifted by the blast, water vapor condensed in the mushroom cloud's cap, and clouds formed by heat from ensuing fires.
In a broader sense, black rain can also describe any rain that is blackened by the presence of smoke particles, fungus spores, or dust in the atmosphere.
Thus, black rain is essentially precipitation heavily polluted by particulate matter, often with a hazardous component when linked to radioactive fallout.