Wikipedia has a useful article on civilization, see here.
When thinking about the survival of civilization we think about civilization as a way of organization that enables intelligent beings to share and use information. This seems fundamental to gain a degree of freedom from the dictates of natural processes. In maintaining civilization it seems necessary that useful knowledge is maintained through time.
Nature demonstrates effortlessly how the biosphere can survive, evolving over billions of years. Whether we can maintain civilizations capable of providing benefit to its members in the long term is less certain.
Civilization is not limited to the civilization those able to access this site live in. milliongenerations.org is founded on the hope that humans will find ways to continue and evolve civilizations. That may include parallel civilizations existing on the planet at the same time.
It may be feasible and eventually desireable to spread to other planets and solar systems. This is NOT the focus of milliongenerations.org, see the motivation.