The Destruction of the Ancient Sith and the Fall of the Old Republic

In the early seasons of The Clone Wars series, we learn about the Mandalorian culture and its history. When Jedi Master Obi-Wan Kenobi confronts Mandalorian extremist Pre Vizla, the latter refers to a historical event called "The Fall of the Old Republic", which occurred a thousand years before the Star Wars films. What is this moment in galactic history? How does it relate to the fall of the ancient Sith, an event which also occurred a millennia ago? Join me as I speculate.