Did you know that the word apocalypse is an ancient Greek word which actually refers to some type of uncovering, a disclosure of knowledge or revelation. Just thought to point that out.
In the sense of the modern day meaning given to apocalypse, an apocalyptic world would refer to an almost completely destroyed earth with little or no resources left for the few survivors. If I was among those survivors of such an apocalyptic world, my life, living, would be of utmost importance to me. No matter how bad any situation is, we always want to keep on living because wherever there's life, there's hope.
However, if we were to draw from a wider scale or perspective, the utmost important thing would be the continued existence and preservation of the human race. Almost everything is possible with humans. Look how far we've come and our astonishing achievements since the first man walked on earth. An apocalyptic world doesn't necessarily mean the complete end of the world. Hence, with the continued existence of humans, we can still rebuild the world to what it once was.