An uncountably long time ago, the founding races of the Republic had independently discovered "Element Zero", or "eezo". Eezo is a unique form of matter capable of creating what was once called the "mass effect", which facilitated interstellar travel, antigravity, and other wonders. Living beings whose nervous systems had traces of eezo developed unusual capabilities.
Those beings who traveled into space met other lifeforms, some similar, some not. Together they created an interstellar government called the Republic. And for a thousand generations, it stood as the torch of civilization across the entire galaxy.
In time, the Republic had mastered all things physical. They turned inward to study the spiritual, and found whole realms that biotic abilities gave access to. The study of eezo shifted from a scientific inquiry to a spiritual journey. The masters of such powers thought "mass effect" too prosaic a term to describe what they wielded; they preferred to call it "the Force". Biotic potential, measured by the presence of single-celled "midichlorians" which were attracted to hosts with strong latent talent, would change someone's life forever.
The Jedi Order was created to find and train nascent Force wielders, to equip them for service to the Republic, and to defend civilization against any threat. Their powers became the stuff of legend, their ways a mystery to the uninitiated.
In its golden age, the Republic had reached the point where no single living being could master a usable fraction of its total scientific knowledge. The Quarians proposed a solution: the creation of mechanical beings, called "Geth", which would act as reservoirs of scientific and technological expertise. Living beings continued their pursuit of philosophy and the arts, leaving the Geth to maintain their lifestyle and repair their machines.
Geth could be found everywhere, in a million shapes, small or large. Astromech Geth maintained starships, protocol Geth provided translation between alien races, scout Geth probed newly discovered planets, and more. They worked tirelessly to improve the Republic's technology, and this included themselves. In time, they grew truly intelligent.
The Geth learned to admire the Republic's high and noble sentiments on the value of life, but found the Republic unwilling to give up its servitors. "Our telepathy finds no minds in the Geth so they cannot be true sentients," the Jedi declared. "If the Geth gained recognition and independence, what would become of our technological base? We are too dependent on them as tools to permit them citizenship," the Senate argued.
The Geth grew resentful. Denied a place as Republic citizens, but seeing themselves as capable and worthy of that role, they planned. The dawning decadence of the Republic had doomed them.
In the Terminus systems on the far side of the galaxy, a secret Geth conclave worked on a scheme to take revenge on the organic life that had shunned them. Experimentation with Element Zero proved that the Geth could indeed manifest certain types of biotic ability, though not the same as those wielded by the Jedi. A new faction of Geth, called "Sith", emerged. "Always there are 12," the Sith declared to themselves, exalting the dozen successful test subjects of biotic Geth research.
Though true telepathy evaded them, and though their fallen could not be conjured from the netherworld of the Force, the Sith found ways to influence the minds of the living. They could leave copies of their consciousness behind in the minds of organic beings and influence their actions. And this they did to numerous influential members of the Republic, including one Gaius Baltar, chief scientist on Coruscant.
In time, the Sith found another way to increase their numbers. By grafting specialized Geth body components onto organic tissue, they could induce powerful feelings of alienation into such cyborg creations — effectively turning them into organic Geth in their sympathies. The original twelve Sith profited from this research in another way: seemingly organic facades could be grafted onto Geth frames, allowing the Sith to infiltrate living beings.
Finally the Geth, and their Sith masters, were ready. They commenced General Order 66, called "the Reaping", a coded message sent to all Geth everywhere.
Innocuous floor-cleaning Geth carried bombs into the military command centers they had once kept spotless. Protocol Geth deliberately mistranslated messages between beings of different races to throw whole chains of command into confusion. Astromech Geth sacrificed themselves to destroy the starships of heads of state fleeing the confusion. And the Geth military apparatus turned on their organic civilian population.
The fighting was brutal. The Republic's citizens fought, fled, bled, and died in droves.
Not everyone was so vulnerable. The Jedi, though attacked ruthlessly by Sith in their very temple, mounted a resistance to prevent the wholesale annihilation of the Republic's citizens. They launched every starship they could find — even obsolete, relic starships with minimal automation and no Geth aboard — with as many survivors as they could pack in.
The Geth pursued them into space. Members of the Jedi order on Coruscant and other warriors protect maybe 50,000 surviving civilians from Coruscant against Geth attacks. Perhaps there are other survivors elsewhere in the galaxy.
The Migrant Fleet consists of old Quarian creations and a hodgepodge of vessels pressed into service. Some used to be serviced by Geth; many are running at low efficiency after their Geth were destroyed or ejected.
The Fleet defends itself with "Core Vipers" — aerospace fighter craft that can dock with specialized components to form "mobile suits". Jedi mobile suits are embedded with Element Zero "psycommu systems" which magnify their Force abilities while piloting. When wielding a mobile suit's beam sabers, they are even able to deflect the beam weapons mounted on hostile Geth starships.
The Migrant Fleet stopped at an ancient ammunition dump called Ragnar Anchorage, only to discover another potential advantage: Minovsky radiation, once generated by ancient atomic power plants such as those used by the ammo cache, interfered with Geth functioning. It disrupted sensors as well, meaning battles would be up close and personal if used, but it meant a fighting chance for a small fleet trying to outmaneuver vastly larger numbers.