From AMS Glossary
(Sometimes referred to as pedestal cloud.) A local, often abrupt lowering from a cumulonimbus cloud base into a low-hanging accessory cloud, normally a kilometer or more in diameter.
A wall cloud marks the lower portion of a very strong updraft, usually associated with a supercell or severe multicell storm. It typically develops near the precipitation region of the cumulonimbus. Wall clouds that exhibit significant rotation and vertical motions often precede tornado formation by a few minutes to an hour.
Fujita, T. 1959. A detailed analysis of the Fargo tornadoes of June 20, 1957. U.S. Wea. Bur. Res. Paper 42. p.15.