You're probably thinking that I'm going to talk about kids and family and all that kind of thing, but I'm not.
Right now the most important thing for the human race is to get off this planet, very soon. With fossil fuels running out and resource wars on the horizon, we really don't have much time left. If we're not living in space by 2100, then we'll probably be living in caves.
Until we have self-sustaining colonies in space, a single major disaster can wipe out the entire human race, or at least throw us back thousands of years to a point where we may well never reach this level again. That doesn't need to be a physical disaster, even a general withdrawal from the real world into virtual worlds could eliminate any further desire to expand into the universe until something comes along to destroy us (be it an asteroid on a collision course, or an aggressive alien race).
Beyond that, we need to spread out across at least a thousand light years to avoid being wiped out by a nearby supernova, which could happen in short order with little warning. The radiation emissions alone could wipe out human life within tens of light years of the supernova.
On the plus side, without venturing into 'Star Trek' and using only believable future engineering, we can manage that in 10-20,000 years and go on to spread across the entire galaxy in a million years. At that point the biggest threat will be the potential future collision between our galaxy and Andromeda a few billion years from now, which will mean a need to expand into other galaxies; a trip which itself could take millions of years. Beyond that... who knows?
Another benefit of expansion out beyond the solar system is that space is vast and the speed of light is low, so anyone who wants to be free is unlikely to be found unless they choose to be. Pick a random direction and head off at 10% of the speed of light and detecting you will be extremely difficult; perhaps at some point in the distant future someone will fill the galaxy with nanotech probes that can cover every single cubic mile, but that itself would be a vast undertaking.
The race to get off Earth before it's too late is going to be tight, and I just hope we win. I can't think of anything more important than ensuring our descendants are still around a million years from now and spread across the galaxy.