The Times of Chaos were a period in which most of galactic political structure broke down as the Fallen Republic fell. Thousands of big and small wars took place simultaneously, and without a central government piracy destroyed most interplanetary trade, causing worlds to be isolated and as a result vulnerable to attack, leading to a viscous cycle of destruction.
Before the times of Chaos, there was a stable galactic environment. Though the exact details are unknown, there were several superpowers (in the Union and Core Hegemony area of the galaxy this was the Fallen Republic 1) ) and these engaged in open trade.
Power was centralised with these superpowers and travel between different parts of the galaxy was comparatively easy - one could be guaranteed they were safe as superpowers maintained order and prevented such things as piracy and other problematic elements. All in all, there was one galactic economy with established trade lanes and a generally free flow of people and goods.
Then, the Times of Chaos hit the galaxy. Nobody knows exactly what caused the times of chaos. Perhaps it was economic downturn, political revolt or the likes. We know that the development of new technologies led to centralised governments having a hard time holding on to their power as pirating became easier and more lucrative.
Regardless of the cause, the Times of Chaos are not a one off event, they did not start at any particular time, but rather started at various times in various places as central governments were more or less successful in maintaining order. Depending on where you were, the Times of Chaos lasted some three to five thousand years.
With no central governments, the entire galaxy became a giant failed state. The intergalactic trade networks broke down, hyperspace lanes were lost and entire civilisations rose and fell multiple times over time. As a result, much historic information was lost. Most people couldn't get out of their home system, let alone their sector, with the possible exception of pirates who in turn fell victim to one another.
During this period many worlds, unable to trade due to piracy, were cut off from one another. As these worlds depended on one another for trade, economic problems arose on an unprecedented scale, sending the entire galaxy into a huge recession from which it still has not recovered. Many worlds faced revolutions and those that did not faced huge social change being locked down into a single system.
This is not to say worlds could not have contact at all in the Times of Chaos. Individuals could travel between worlds at great danger and messages could be exchanged, but with nobody to repair infrastructure and no option to trade, many worlds declared the intergalactic community irrelevant as it had little to offer them beyond exchanging niceties - not to mention that many people blamed “the other worlds” for the Times of Chaos.
Over time, technologies changed at different paces in different places, but about a century ago the technology developed to a point where centralised governments could once again hold power over quick-witted pirates and where decentralised groups and rag tag bands of pirates were no longer at an advantage. Powers such as the Confederacy of Excaria and the Holy Heimgolian Theocracy used these new technologies to construct fleets and wipe out piracy in their sector, setting up trade with one another. Like them, other new powers arose dealing with piracy locally to allow access to new galactic resources.
This improved access in turn boosted the economy of these worlds which led to the governments that had brought down the pirates rising in power. Soon, they would run into neighbouring states.
Recognising the cost of a full scale war - the destruction of all the advantages gained - some fifty years ago several local powers founded the Union, with Unity as its capital planet. Together they eradicated piracy between them, restored the Bozzy Spine to allow easier trade between them and slowly but certainly new worlds who had been previously cut off were able to join the Union, forming the institution it is today.
The Jedi were certainly a power to be reckoned with, but even they did not have the power to stop the Times of Chaos. Jedi Temples were destroyed in revolutions, raids and wars, and individual Jedi were cut off from one another by the new conditions. Isolated and subject to forces beyond their control, ancient teachings were lost as the Jedi valued the preservation of life over the preservation of knowledge and would rather save the children hiding in their temple then carry of Holocrons with secret knowledge.
However, the Jedi did survive the Times of Chaos, and through long distance communication and occasional dangerous trips, some form of Jedi Council was held, made up of individual Jedi Masters rather than being any centralised authority of sorts. Various sects and subgroups of the Jedi formed and splinter groups split off, never to be heard from again.
When the new powers started gaining on the pirates, the Jedi were instrumental in getting governments in power and they were the key instigators in forming the Union, lobbying with leaders about the cost of war and the benefit of cooperation. As a reward for their efforts, the Jedi were granted a Jedi Temple on Unity and they still hold great political influence on many Union worlds.
Like the Union, other places too had their rise of central authority figures. The Core Hegemony, and arguably the Hutt Families, ended the Times of Chaos in their sectors by assuming centralised control. But many sectors still remain in the hands of pirates as they are too far away for super powers to bother - here, the Times of Chaos are still raging. Arguably the first area where the Times of Chaos ended is with the Mandalorian Fleets, who have a long established tradition of ruling their area, though since the Mandalorians are raiders and pirates, one could argue that they are the very representation of the Times of Chaos.