In the original concept, the mass relays are powered by eezo cores. The radiation emitted by the eezo cores, which is known as dark energy, is shortening the life of stars, and will eventually destroy the galaxy. (This is similar to the episode "Force of Nature" in which the warp drives of starships are tearing the fabric of space.)
So, anyway, the creators of the mass relays realize their mistake, and seeing that they couldn't solve the problem on their own, they become the first Reaper - Harbinger. With each cycle, the Reapers grow in number and, with each nation, they can find new ways to approach the crisis. The Reapers harvest the species that has the most value in that cycle.
Initially, for this cycle, this species would have been the asari, but because of Prothean subterfuge, the cycle was delayed by two thousand years. The humans, because of our genetic diversity and our ability to be innovative problem solvers, replace the asari as the species with the most value.
Then the choice at the end of the third is as TheGodBen describes - humans become a reaper, or humans say no thanks, we will find a solution ourselves.