Probably when we'll solve the problems of artificial intellegence,
interstellar propulsion and precise astronomical observation allowing
us to see and analyze small planets around relativly close by star systems...
Peace and long life.
We are the von Neumann probes.
Think about it; our most advanced technology is being used to explore our solar system and universe. We're satisfying the exact purpose we were originally designed for by doing exactly what we are now.
It began when the planet was "seeded" billions of years ago with single-celled machines (made of organics as opposed to raw metal oxides) capable of mutating. The mission: find an environment capable of remaining stable long enough for you to evolve and communicate back to Origin. "Our" planet may meet that requirement, provided we can link up before the next major impact or other catastrophic event.
What else can explain the uniquely human need to explore environments we're not physically able to alone? There was no reason for us to be keenly aware of what drove us, we just did it. It's in our code so it comes naturally :)
Incidentally, all other animals came from this initial seeding as well. It's almost as if the entire biosphere is one large machine with the exploration of space as it's ultimate goal. Over billions of years, the biosphere has finally made it to the point where it can extend outside the planet.
It may not be long now before this "mission" is accomplished. What we may want to ask instead is "what then?"