The point is fairly simple. It's only natural to want to protect humanity in case of a massive world ending event, and Vaults were a means of containing a massive amount of people into safety.

Of course you can't fit all of humanity into them, so those who were left outside... well many died, some mutated. Those who survived without protection lived in areas where the pockets of radiation were minimal, in comparison to the major cities. And those people are the ones who shaped the world in the wake of nuclear holocaust.

It's not going to be the world as you remember it, but it's still alive. Still surviving, making the best of the worst. Most of the Vaults have already been opened and abandoned for a long time though.