The Republic Dark Age was the term given to the last century of the New Sith Wars, from around 1,100 BBY to the Ruusan Reformation of 1,000 BBY. During the Dark Age, the Republic, in the eyes of later centuries, had essentially ceased to exist.
Since the start of the Draggulch Period in 2,000 BBY, the Republic had been in decline. During the series of conflicts known as the New Sith Wars, thousands of worlds were abandoned to the New Sith Empire, while more were abandoned during the Republic's retreat. Thousands of longstanding corporations went bankrupt, lawlessness spread as the Republic government became increasingly overburdened and ineffectual, and numerous mines of valuable minerals dried up. The collapse escalated following the Sith victory at the Battle of Mizra in 1,466 BBY.
However, all these events were merely a prelude to the Dark Age. The Senate granted almost all of its authority to the Supreme Chancellor, many of whom were Jedi at that point, such as Jedi Master Genarra. Throughout the galaxy Jedi joined in bands to defend individual worlds, and even regions of space, from Sith, pirates, slavers and warlords. In some regions, the Jedi supported existing governments, though in others, Jedi became rulers themselves in order to protect the population from external threats. The more troubled regions of the galaxy were divided by the Supreme Chancellors into Jedi baronial sectors, in an attempt to coordinate the continuing war against the Sith. Although the unity of the Sith seems to have been broken by infighting, and the ongoing conflict was officially portrayed as merely a series of clashes against an illegal organization, the situation wore down the Republic Navy and Army, which likewise fell under increasing Jedi control.
The Republic could no longer afford to maintain the HoloNet beyond the Core Worlds, so communications between worlds outside the Core had to be maintained through couriers. Even worse, a galaxywide epidemic of Candorian plague killed off as much as two-thirds of the population of some worlds.
As already noted, it seems that the threat from the Sith may have been much diminished compared with previous centuries, but at the end of this period, around 1,010 BBY, Lord Kaan reorganized the feuding Sith into the Brotherhood of Darkness, and embarked on the last of the New Sith Wars, sometimes known as the Light and Darkness War. Republic forces led by commanders like Hoth, a Jedi Master and General, won some notable victories, initially driving Kaan's forces from their stronghold in the Cloak of the Sith, but the Sith reconquered their ancient capital on Korriban, and also struck deep into the Core Worlds.
For the final two or three years of the war, however, much of the attention of the Jedi and Sith was focused on the planet Ruusan, near Kashyyyk, where the entire Brotherhood of Darkness fought the Jedi who Hoth had formed into the Army of Light in a protracted series of engagements.