The Four were part of a secret moon launch in 1961, a project called Artemis. On their way, they encountered a rift in the fabric of the universe, which sent them to another world. The inhabitants of this world were vastly powerful, and very paranoid. They perceived the Earth as a threat, due to its unfortunate tendency to breed superhumans.
Dowling made a deal with the inhabitants of this world. He and his companions would be endowed with incredible superhuman powers, and in return they would use their powers to suppress the emergence of superhuman powers on Earth. They were given fifty years to prepare, at which time their earth would be destroyed and the Four would be free to explore the Multiverse.
Upon returning to Earth, The Four used their powers to manipulate governments and scientists. They used assassination, subversion and oppression to use their world as their laboratory. They collected and destroyed artifacts and beings that would have otherwise advanced humanity immeasurably, and razed entire worlds in order to store their hoarded treasures.
Their primary adversary has been the *Planetary* organization, specifically Elijah Snow. While they enjoyed the challenge that Planetary provided, they knew they couldn't allow the group to threaten their plans.
So, as their fifty-year deadline approached, Randall Dowling abducted Snow and made him submit to a series of memory blocks that would prevent him from disrupting their final plans. In return, Dowling said, they would allow Snow's colleagues to live.
The remainder of Planetary, however, took the risk and returned Snow to the organization. Once he regained his memory, Snow turned Planetary towards the single end of destroying the Four.
The Four are directly modeled off Marvel's Fantastic Four - the characters and their powers are similar, as is their origin. The difference, of course, is in the Four's use of their powers to suppress the progression of humanity, whereas the Fantastic Four are much more benevolent.