the meek shall inherit the universe

Humans, at first glance, do not appear to be well-designed for survival. Our lack of fur, lack of claws or other natural means of attack and defense, slow breeding times, and our lengthy, costly infancy and childhood (when babies and children are resource drains on adults) all should have combined to make us a biological curiosity, inhabiting some exotic location where conditions were just right for our continues survival. In this way, we would have been rather like the frill-necked lizard, or the polar bear, or various deep-sea-dwelling fish.

Instead, humans have spread from the African savannah to every continent and every climate on the earth. We do this through a singular ability: engineering. Certainly, we are still fair game for predators in many places in the world, making, as we do, juicy meals full of protein and calcium. However, we have managed to win the predator-prey game with most of our larger predators, and many of the smaller variety too, such as smallpox.
We have spread to every part of the earth and harnessed the resources of minerals, plants, and other animals to further our own survival. The next step are the empty horizons of nearby planets and Moons.
The planet Mars and the moons Io and Europa have been nominated as possible locations of future human settlements. But their current environments are hostile to humans and currently don't support life. Could we transform them before moving in? Possibly. This strategy is known as terraforming. Such a process would probably take hundreds or thousands of years, and would involve causing permanent changes to the atmosphere, melting the polar icecaps on Mars, and fostering plant life.

Robert Zubrin, in Entering Space: Creating a Spacefaring Civilization, makes the case that this is the natural development for the human race. He points out that the period of European colonial expansion was correlated with unprecedented advances in science, arts, and democratisation, and suggests that human conquest of space, by allowing mankind the freedom to experiment and innovate in new environments, will have similarly beneficial effects.

Michael Griffin of NASA says space travel will be dangerous. He predicts that despite the likelihood of death, people will still travel into space. It fulfils the human need for exploration, conquest and hope in a way that travelling to new continents did in the era of European colonization (and at all times that humans have travelled to new parts of the Earth). To back this up, Griffin points out that the risk of dying whilst climbing Mount Everest is 10%, yet people still continue to climb.
But who will leave the comforts of Earth for the perils of space? If history is any guide, people from all walks of life, but they will be disproportionately the poor and dispossessed: people with nothing to lose.
Wealthy European governments and corporations bankrolled European expansion, but it was poor ethnic groups suffering from persecution (the pilgrims), deprivation and famine (such as the Irish) or the victims of the ravages of war (such as the Italians) that moved in large numbers to countries such as America and Australia. On the other hand, extremely hostile locations such as Antarctica are still populated entirely by government run organizations.
Only after a planet or large moon has been terraformed or otherwise deemed fit for human life will true human settlement, in all its messy, tumultuous, mix of despair and hope take place on a large scale. Given the current pace of technological change, and estimates of the huge time frames involved in terraforming, that will not be until several centuries in the future.
But when it does, as before, the poor, or in the Biblical terms, the meek, will once again shape the future, and inherit whatever inviting part of the Universe we happen to find. Unfortunately, the meek have a habit of staging rebellions and declaring independence, so the dream of a galaxy-wide enlightened civilization, ruled by a benevolent centralist government will probably remain a fantasy of Star Wars movies. Instead, humans will continue to do all the things they do here on planet Earth: love, hate, despair, hope, strive, and quarrel. As the old saying goes: all you have is what you take with you.