The most common theory is that the Forerunners were displaced humanity, divergent descendants of the human race. This theory fits the 2001-2009 era fiction, as well as real world science, and avoids the possibility of any inconsistencies with the story or its setting. It also makes sense that the Forerunners would hide their true appearance, obscuring it with their own relic technology and encouraging their ecumenical allies to believe they too could ascend to godhood by following in their footsteps, as the final triumvirate of Hierarchs desired.
The Forerunners had a system of societal organization called the Mantle, which was built around the idea that it was their moral duty as a culture to hold stewardship over the other lifeforms they encountered and incorporate those civilizations into the Forerunner Ecumene. This was achieved in part by utilizing Forerunner technology to interfere with and shape the development of lesser species, but also by providing a path to godhood for any willing to follow it.
This belief system led to a society that was highly militarized, requiring all males to undergo extensive genetic modification as a form of biological augmentation and undergoing a ritualized series of physical transformations as a mark of passage into adulthood. They also created a rigid caste structure, wherein each male and female was assigned to a rate in which they could specialize into a given profession.
As a result of Spartan John-117's mission to the Ark and other ONI missions, UNSC scientists are slowly beginning to build a picture of Forerunner society and culture from ruins of Forerunner cities, installation sites, drifting starships, and long-abandoned installations like Halo Installation 04 and its attendant shield worlds. These discoveries have also revealed cryptic data strings that are presumed to be attempts at communication by the rogue AI Cortana.