The remake dramatically expanded their story to make them more significant, but... (spoilers follow)
It's revealed that they are displaced space alien refugees that fled to this planet, and that the planet rejects them because they're foreign. No matter how many generations of them have lived here, when any member of the race dies, their soul is not accepted into the planet's lifestream, and the whole race is therefore forced into a permanent, ghoulish undeath. Jealous of the planet's rightful inhabitants and filled with vengeful rage, the Gi create the black materia, a weapon to destroy the world and everyone in it.
I can't help but think...why does this sound like an allegory for someone's awful conspiracy theory about the Jews and the atomic bomb or something?
I mean, it's not much of a stretch to observe that "they moved here but they don't belong here, and they plot to destroy our home" is a narrative lots of right-wingers have about any number of real-world people, right?