The story
From Augean (“pertaining to Augeas”) + stables. Augeas was a legendary king of Elis in Greek mythology who owned numerous divine cattle (3,000 head, according to some later retellings) which produced a huge amount of dung in stables that had not been cleaned for over 30 years. The cleaning of the stables was the fifth of the twelve Labours of Hercules, which Hercules achieved by rerouting the Alpheus and Peneus rivers through them.
Etymology from Wiktionary, CC BY-SA 4.0.