Foom, or "AI foom", is an informal but popular shorthand term for a hard AI takeoff -- or, as rationalwiki puts it, it is short for a "recursively self-improving Artificial Intelligence engendered singularity". It is generally viewed as a extremely dangerous thing, and the term most likely comes from an onomatopoeia of a mushroom cloud.
Originally 'foom' was written in all caps, but that was dropped fairly quickly once it came into common usage in futurism circles. Foom is most often a noun, although it may be used as a verb.