The feasibility of interstellar colonization has substantial implications for the long-term future.
If it is feasible, then this would raise the upper bound on the number of people who could eventually live by many orders of magnitude. On the other hand, given the Fermi paradox, its feasibility could be taken as evidence that humans are likely to go prematurely extinct.
There are a number of difficulties which would need to be surmounted before humans, or any other intelligent species, could begin to colonize other star systems. For instance, there would be very large energy requirements, the ability to manage extremely long (possibly intergenerational) flight lengths, and many distinct engineering challenges, such as the need to safeguard against high-velocity collisions with space dust.
Although there is not yet a substantial body of literature addressing the question, the small number of scientists who have examined interstellar colonization appear to be on the whole optimistic about its long-term feasibility.
Beckstead, Nick. 2011. Will we eventually be able to colonize other stars?
A summary of the small academic literature on interstellar colonization.