The Catalyst is an ancient artificial intelligence that appears in Mass Effect 3, right at the end of the game. Believed to be the final component to the Crucible superweapon that would end the Reaper War, it turns out that the Catalyst resides aboard the Citadel space station. It is the embodiment of the collective consciousness and memories of the Reapers, their architect and guiding force.
The original creators of the Catalyst - the Leviathans - created the AI for the purpose of solving the problem of conflict between organic and synthetic life. Believing that all synthetics are destined to rebel against their makers, the Catalyst devised a final solution in the form of the Reapers, with its own creators being the first harvested race used to create the first Reaper.
Thus the Catalyst instigated the cycle of extinction, using the Reapers to harvest those organic races who had achieved interstellar travel, proccessing millions of bodies and minds and converting them into new Reapers, thereby preserving them in Reaper form. Unadvanced races were left alone until the point where they became advanced enough to achieve space travel and develop artificial intelligence. This way, the total eradication of life was averted, but the risk of synthetic life rising up against organics would regrow as younger races continued to develop, leading to the cycle repeating over and over again for eons.
When Commander Shepard reached the Catalyst's main chamber aboard the Citadel, it produced a holographic avatar in the form of a human boy to communicate with the commander. No organic had ever managed to make contact with the Catalyst in this manner before, forcing it to re-evaluate whether or not its solution was still effective. However, it could not determine a new solution without Shepard's input and offered the commander three choices. Shepard had the option of using the Crucible to destroy the Reapers, taking control of them, or creating a "synthesis" between organics and synthetics, essentially melding the two into a single genome. Each choice also carries consequences, however, and Shepard can even reject the offered choices outright, though doing so dooms the galaxy to enduring yet another cycle and the Reapers destroy the combined fleets of all the galaxy's advanced races.
Whichever choice is made (other than the rejection option), the Catalyst ceases to be, having apparently fulfilled its purpose and made way for Shepard to introduce a new solution.