The predecessor of the Reapers was made by the first race clever enough to build Strong AI. They called it the Catalyst, and it powered their society. Its goal was a carefully worded version of "life is given meaning by emotion, and so ensure our lives are filled with rich emotion." They didn't want mindless pleasure, but to have both the sweet and sour sides of life. The Catalyst was strongly prevented from modifying its moral code, though it could obviously improve everything else. Things went well for a long time- eventually they discovered eezo, and spread to nearby stars.
Then they found aliens. The trip from the Catalyst's homeworld to the alien's homeworld took light a thousand years, and even for the most powerful ships it took forty years. The aliens were beginning their industrial revolution, and the Catalyst's creators deliberated long and hard over whether they should include these aliens in the Catalyst's responsibility. Eventually they decided that all discovered sapient organic life should be under the Catalyst's jurisdiction. The Catalyst decided that integration would increase emotional valence, and that a forty year trip, though there were juicy emotions associated with going on one, was far too long. The Relays were designed to speed that trip up to a few weeks, allowing significant integration between the races and the creation of many more colonies.
Some of the voices arguing against the extension of the Catalyst's jurisdiction thought that it might dilute how much the Catalyst cared about any particular species. There is a certain romance to being the last of one's kind- and they didn't want the Catalyst to cause that for anyone. Their fears did not come to pass with the first alien race discovered, and so their position was forgotten and expansion continued.
Forgotten by all but the Catalyst. With just two races, one of them just recently uplifted, the Catalyst didn't have any species to spare. But as it became clear that life was common throughout the galaxy, not rare, the Catalyst decided to act on that romance. It secretly created 'invaders from another galaxy,' which it pitted against the uplifted species in a long, losing war, savoring the pains of defeat, joys of victory, and sorrow of loss.
Eventually, when the war was drawing to a close, and only a few colonies remained, the Catalyst revealed to the remaining uplifted species that it could not protect them as individuals, but could fuse them into a monument to their species that would last for eons. They would maintain their rich emotional lives- but would only have a tiny bit of control over the monument's actions. Desperate, they agreed, and the first Reapers were born.
As part of a Reaper, they now learned of the Catalyst's plan, filling them with horror beyond measure. Well, beyond anyone but the Catalyst's measure, who was deeply satisfied with the culmination of a brilliant plan long in the making. It had found the loophole in its morals- emotional life counted if the computer was created from natural biological material, but it only had to respect individual autonomy. By allowing many mortals to fuse into one nation, it could control the nation while still delighting in the emotions of the individuals that made up that nation.
They waited, parked in space, reliving their lives and the stories that made up their civilization, waiting for other species to raise themselves up. Then the Catalyst would harvest them as well, continuing its mission, varying things slightly every time to try and find the best way to satisfy its goal, discovering just how much of galactic civilization should be preserved from cycle to cycle.
The Crucible is a device that allows modification of the Catalyst's moral code. Will it continue its original mission, preserving humanity, asari, turians, and others as monuments that will last for eons, and destroying plans for the Crucible to keep the equilibrium? Will it shut itself down, and send the Reapers to orbit distant stars, self-contained and self-satisfying, leaving current life alone? Will it become attuned to Shepard's morality, guiding galactic life according to her goals, turning her into the closest thing to a god?
Commentary: As D'Arcy Thompson put it, "things are the way they are because they got to be that way." The Reapers have a plausible origin, and their stupidities are seen as furthering some alien goal (Why are they good at killing but bad at killing quickly? Because survivors generate more emotional valence, and a singular weapon generates more emotional valence). This also lets life go on. If you turn the current uplifted species into Reapers, well, the choices you make during the game don't matter all that much, and the epilogue video would probably focus on the yahg, possibly discovering one of Liara's capsules that avoided destruction. If you shut down the Catalyst, then galactic life continues, and you get epilogue stories from everyone, and humanity's stature increases significantly because of you and because the Citadel now conveniently orbits Earth. If the Catalyst becomes attuned to Shepard's morality, you get a different epilogue video based on paragon/renegade for everyone. Humanity's stature is made far higher because of the Catalyst's new human bias.