There really isn’t an economical explanation for why a civilization would engage in long-range interstellar colonization.
To begin with, though, let’s look at interplanetary colonization. Why, for example, would someone fund the establishment of a permanent colony on Mars with the intent for it to become eventually self-sustaining? It’s not to relieve population pressure. Stuff is so ridiculously expensive to get into space that you’d be better off (from a monetary perspective) paying the people to live in the Sahara. It’s not for resources; asteroid mining is almost certainly a feasible economic opportunity, but the cost of lifting resources into orbit is again the obvious barring factor. It could be scientific, but scientific missions wouldn’t need to be self-sustaining or long-term. Perhaps a stint of 20 years on the surface. It could be done by a separatist group (plenty of people want to go start small settlements in the wilderness), but even if the money was raised (which is unlikely), the colony will lie on the fringes of human society. They would probably be unable to arrange a return trip, even if they wanted to, and nobody else (except more fringe groups) would want to continue colonization.
There is one argument that seems reasonable: outposts could serve as refueling stations for outbound craft (asteroid mining operations, etc). However, it would make more sense to pull these resources from asteroids and place an automated fuel refinery in high orbit around Mars (or other suitable candidate).
Many of the reasons listed above carry over to interstellar missions. The only difference is that groups would have much more trouble raising money for the mission, and that now lifting stuff into orbit isn’t the only tough part, but also accelerating your spaceship to a speed which makes for a bearable trip length.
Here are some scenarios where we do send a colonizing mission: we discover evidence of alien life, or the ruins of an alien civilization. It would only make sense to send a colonizing mission. Sending a scientific detachment with a planned return trip would be so expensive that it wouldn’t be worth it. I mean, it would be worth it, but nobody would be able to raise the funds.
Another scenario in which most of the above arguments go out the window: we build a space elevator. That removes the gateway for getting into orbit. We could expect many more people accessing and living in orbit (because they feel like it and the price is low enough). Once the population already flying around the solar system reaches a critical mass, colonizing Mars becomes a trivial step.
Actually, it came to me after I wrote this post that there may be one reasonable explanation for colonizing Mars: if we fail to find an economical way to increase biomass production either on Earth or in space, we will need large tracts of arable land. Terraforming Mars would provide this. However, the cost of lifting and storing that biomass may make it less preferable to aerocultures in orbit.