The Next Great Ice Age is an era that leads into the Next Glacial Maximum, that begins around c. A.D. 12,000, and ends c. 5 million years, A.D. At this point, humanity is facing extinction. The best of scientists from that era came together to solve the problem, but in the only logical solution seems to be relocation to another habitable era by time-travel vehicles. At first, unmanned probes were sent out to explore different locations, in different eras, as well as to test the technology. But, without the systems to fully explore the environments, they built a time-traversing aircraft to explore them with human supervision. The daughter of the era's leading scientist volunteered for the mission. The mission is ongoing...
Nothing much is known about the civilization of this era, besides that it is technologically advanced. It is implied that logic and scientific reason replaced passion and superstition (although, this might just be from C.G.'s sheltered, scientific upbringing). C.G has noted that the most "fun" she had was at a "state-run recreation facility", which implies (besides the fact that C.G. has never had fun in her life) that the future is boring and regimented (possibly do to the strain of resources that comes with a growing Ice Age).
It is likely that the population live in arcologies — large cities with self-contained environments.
Cultural Notes About the Far FutureEdit
In real life, a future like this would be far removed from the modern era. Being around ten millennia into the future, it would be highly unlikely that elements of the modern culture would be retained. This includes most works of fiction, music, social standards/values, religious believes/practices, and to a greater extent: language. This is not so much people abandoning these things, but just the progression of cultures over time. This would also apply to human genetics, as evolution (and possibly genetic engineering) would slowly evolve humanity something noticeably different (to what, is highly speculative). Of course, none of this is touched upon in the show, as that would complicate the show (language/cultural barriers; the principal character looking too much like a space alien; etc.).