As a result of the events of Mass Effect 1, a small but influential group of humans and other council races become aware of the impending Reaper invasion. They fund the Andromeda Initiative in order to preserve the major Milky Way species in the Andromeda Galaxy – in case Commander Shepard fails to stop the Reaper Invasion.
The Andromeda Initiative recruits colonists from among their friends and family who have been awakened to the Reaper threat. They launch a campaign to convince others to join the Initiative. Of course, they are not taken seriously and are portrayed as scam artists trying to scare vulnerable people into giving up their life-savings to the Initiative. Nevertheless, they manage to convince enough colonists to join the expedition. These colonists are true believers in Command Shepard. They have been red-pilled as to what's really going on. They take the Reaper threat seriously. They want to get the hell out of the Milky Way before shit hits the fan.
The colonists arrive in Andromeda 600 years later. They discover that dark energy is tearing up the galaxy. This scourge of dark energy has consumed entire star systems, tearing apart stars and planets atom-by-atom through the warping of time and space. This warping releases massive amounts of ionizing radiation to nearby star systems, thereby wiping clean any and all signs of life within these systems.
The Nexus, and several of the ark ships (which contain colonists in deep hibernation), are hit by this ionization radiation, which fries their computer systems. They lose power and navigation. The ships careen into asteroid belts formed from the remains of star systems that have been consumed by the scourge. This severely damages the ships and the Nexus, and they drift apart.
The humans manage to restore their ark. They have lost contact with the arks of the other Milky Way species, as well as the Nexus. The human ark attempts to locate the others. In doing so, the humans encounter star system after star system that has been afflicted by the scourge. They cannot go near these star systems because the radiation and the warping of space and time would tear them apart.
After months of travel, the human ark ship, now running low on fuel and supplies, manages to discover a star system that has not been affected by the scourge. The star system is home to a desert planet with a heavily polluted atmosphere. It is inhabited by a collection of destitute native alien species living in what appears to be a planet-wide ghetto. The humans attempt to make contact in order to re-supply their ship.
Upon landing a shuttle on the planet, the aliens react, at first, with fear and reverence. It is clear that this disparate collection of alien species are stuck in the industrial age, their most advanced technology being nuclear power. Upon learning that the humans are not affiliated with what the natives refer to as 'the Kett', they become hostile and attempt to hijack the human shuttle in order to board the human ark. The humans manage to escape, but not before losing some of their crew to a criminal gang that is holding them for ransom.
The humans must either negotiate with the locals through careful diplomacy, or attempt a rescue. Either way, the hostage situation is resolved. The humans, through their diplomatic and/or military prowess, are able to establish their dominance over the native species. The humans learn that the natives are desperately trying to escape their dying planet in order to find a more suitable world. There is constant in-fighting amongst the various alien species, life is brutal, and they have regressed technologically to pre-FTL times. Hence, they were desperate to hijack the human ark ship.
The humans also learn that the dying world is really a concentration camp wherein various species throughout the Andromeda galaxy are uprooted from their homeworlds and thrown together onto the same, dying world where they have no means of building an FTL-ship to escape their prison. The Kett is the dominant force in the Andromeda galaxy. They are the ones taking over what few habitable worlds remain in the Andromeda galaxy, and are pushing out every other species.
The humans learn that the reason why the Andromeda Galaxy is in such bad shape is because of a major war between two superpowers. Without the Reapers periodically wiping out every advanced civilization, the Andromedan natives are able to develop to such heights of technological achievement that they invented a doomsday weapon capable of wiping clean vast swaths of the galaxy. This doomsday weapon effectively re-creates the big bang, and creates a huge amount of residual dark energy that greatly accelerates the space-time expansion of the galaxy to the point where the nuclear strong force cannot hold atoms together. This unintended side-effect gets worse with time, and the dark-energy fallout will continue to spread and will eventually consume the entire Andromeda galaxy (in a few thousand years or so).
The Kett is the 'victorious' superpower, yet even they have suffered tremendously. Their Empire is reduced to an irradiated ruin, and they lost their homeworld. As a result, they have lost much of their technology, but they have retained basic FTL-technology. They rely on a series of gates (Mass relays) to travel large distances, though they have lost the knowledge of how to construct these gates. In fact, most their scientists and engineers have been killed off during the great war, and then the ruling Kett regime killed off the remaining few geniuses for fear that they might plot a coup. Thus, the present day Kett are descended from the surviving military hierarchy and have little to no interest in science and technology. As a result, they have regressed technologically.
After learning all this, the humans realize that colonizing the Andromeda Galaxy is out of the question as the situation here is worse than back in the Milky Way galaxy (at least you can fight the reapers – you cannot do anything about the fallout of dark energy permeating throughout Andromeda). They decide to turn back and go home, but they are low on fuel and supplies. The natives on the ghetto planet have none to offer. All they have is fossil fuel, solar power, nuclear power, but no element zero or any of the high-tech fuels required by mass effect technology. This is when the humans learns that not all Ketts are equal.
Kett dissidents are also rounded up and dumped onto the ghetto planet along with every other species. These Kett are hated by the other species and face significant racial discrimination, hostility, and outright violence. However, it is these Kett that the humans must recruit as allies in order to learn more about the Andromeda Galaxy – where the habitable worlds are, what are the Kett defences, strength of Kett Empire, and where to re-supply.
The humans must either help the Kett dissidents make diplomatic peace with the other native species, or help the dissident Kett rise to military dominance. This is the only way to gain their trust. Once the humans have their trust, the dissident Kett direct the humans to a planet with few defences and plenty of supplies, including fuel. Still, the human ark alone is insufficient to take on the Kett defences guarding the planet. The humans will need allies to assault the planet.
The dissident Kett have maintained contact with their comrades still serving in the Kett Empire. Through these contacts, the dissident Kett learn of the fate of the other colonist Ark ships as well as the Nexus – they have all been captured by the Kett Empire.
It is at this point in the game that the humans must make a major decision. They must either rescue their Milky Way allies, and their combined force would be sufficient to assault the Kett supply world, or the humans can focus on forging a stronger alliance with the dissident Kett and other native andromedan species. There is not enough time to do both because the Kett Empire is working fast to repair the Nexus and the other arks in order to flee the Andromeda galaxy to colonize the Milky Way galaxy. Rescuing the Milky Way allies first would alert the Kett Empire and cause them to swarm in and overwhelm the human ark, making it impossible to establish ties with the dissident Kett.
Abandoning the Milky Way allies would result in the extermination of all Turians, Asari, Salarians and Krogans as soon as they are no longer useful to the Kett (the Kett need them to reverse engineer Milky Way technology). Rescuing the Milky way allies would mean the humans lose out on a powerful weapon the dissident Kett promise would be useful against the the Reapers – the doomsday weapon that nearly destroyed the Andromeda galaxy. A single use of such weapon would not destroy nor destabilize the space-time fabric of the galaxy, and it would be sufficient to wipe out the Reapears if they could be drawn into the same general area of the galaxy (i.e. When they come out of dark space and pour through the Citadel mass relay). Millions of such weapons detonating simultaneously would destabilize the space-time fabric of the galaxy.
Either way, the humans gain the allies they need to assault the Kett supply world. The Khett are alerted to what's going on. They swarm in. Now it's a race against time to refuel and resupply as quickly as possible before they are overwhelmed.
(If Milky Way allies are rescued)
After an intense battle, the humans and their allies manage to hold the line long enough for the Nexus and the arks to power up and leave the Andromeda galaxy.
(If Milky Way allies abandoned)
After an intense battle, the human and dissident-Kett alliance overwhelms the Kett forces defending the Nexus and the other arks. The Turians, Asari, Salarians and Krogans have been exterminated. Their arks have been restored, and refuelled. The humans refuel their ark, their Kett allies board the other arks, and they prepare to leave for the Milky Way galaxy. Just before leaving, the kett allies reveal that the Kett Empire has maintained a small stockpile of pre-war doomsday weapons. They take this stockpile with them back to the Milky Way Galaxy.
In the epilogue, the humans and their allies arrive back in the Milky Way Galaxy 600 years later. It has been 1200 years since they left. The Reaper invasion has been completed. All the Council races, their homeworlds, and their affiliated allies have been culled. Command Shepard has failed. After travelling from system to system, they happen upon a signal left by Liara. The signal leads the humans to an underground bunker containing a VI, much like vigil, that explains what happened.
The Crucible was a lie. It was yet another a Reaper ploy, much like the Citadel, to lure the resistance into a trap. The Crucible, upon activation, served as a powerful amplifier of the Reaper indoctrination signal. It completely and totally indoctrinated every living thing within the vicinity of a mass relay. The humans realize that the indoctrination theory was true.
The Reapers have restored the Keepers back to their original function. In the next cycle, the Reapers would pour through the Citadel mass relay and start their invasion from there, as opposed to invading from the edges of dark space.
The humans and their allies rebuild their civilization. They plan for the next Reaper invasion. This time, they'll have a fifty thousand year head start. And, if allied with the dissident Kett, they'll also have a doomsday weapon waiting for the Reapers when they arrive.