Eventually, when our sun begins to die out it will grow and expand. It will then eat up our planet. The human race will be extinct once this happens, unless they find another habitable planet to relocate to.

With current technology it will take a few light years to get to the nearest star. Many generations of humans will live and die on board spacecraft that attempt to travel that far. But if they make it, it's going to be another Earth...we probably won't live long enough to find this out ourselves.