What has created the society that exists now? What is hinted at? What is it called?

The society now in existence, called Gilead, apparently resulted from evidence that the human race was dying out. Due to extreme pollution, many people became sterile and could no longer have children, and those who could often had children born with terrible birth defects, defects with which those children could not survive.
Once the population could no longer continue to replace its numbers, many people became even more concerned. At this point, Congress was overthrown, many political leaders were assassinated, and a new kind of government was founded. This new society was organized around which women could reproduce and which could not, as the new leadership believed that men could not be "sterile." For some of those who could not bear children, a place was found. Many were shipped away to certain death. For those who could produce a child, they were offered a chance to do so or to be carted away. A Biblical precedent had been set for a maid serving as a biological mother of a child which would be raised by her master and mistress, and this is how the handmaids come into existence.