The fifth labor of Hercules was to cleanse the stables of King Augeas. Augeas of Elis had an immense heard of oxen whose stables had not been cleaned in thirty years. To complicate the matter, his fields were so large that many other animals were brought to live and graze in them.
Hercules was challenged to completely clean the stables in only one day. He accomplished this by tearing a hole in one side of the stables, then in the other side. He diverted the waters of the Alpheus River through the stable to clean out all the mess left by the many large oxen.
When someone has to clean up a giant mess, it can be referred to as "cleaning the Augean stables". This is sometimes used to describe the work of a new government trying to come in and clean up the work of a preceding corrupt government.