When we think of interstellar travel, we think of powerful starships whizzing through space. Or, perhaps, we think of huge ships-- space arks-- that take centuries to travel between stars. In that case, the people who arrive in the new solar system are the descendants of those who left the old one. Either case presents interstellar travel as dauntingly difficult.
Which, of course, it is. All space travel is difficult and dangerous. That should become less so in the centuries to come, just as sailing the oceans and flying through the air have largely been mastered. If the human economy expands beyond Earth, extraterrestrial resources will be used. That will mean mining asteroids and comets. Such mining could lead to hundreds or thousands of small communities, scattered throughout the Solar System, living on small bodies and constantly on the lookout for new sources of water ice and other volatiles, and metals. The leading edge of that settlement will tend to move farther and farther away from the Sun, deeper into space.
A spherical collection of such bodies that astronomers call the Oort Cloud surrounds the Sun, Some astronomers say the Oort Cloud may extend halfway to the nearest star, which is the Alpha Centauri multiple star system. If Alpha Centauri has its own Oort Cloud-- and some comets almost certainly come in from outside our system-- small bodies orbiting on the edges of the two realms likely intermingle.
Small human communities drifting farther and farther out, in search of economic gain, or new knowledge, or more freedom, or adventure, or simple isolation may eventually ease into the gravitational influence of Alpha Centauri. One of the signal events of human history may occur unnoticed by anyone.