Setting overview

It's been many centuries since humanity has spread among the stars. Exactly how many, it's hard to say, between all the different calendars and inevitable data loss. But general consensus is that we're roughly as far from the 21st century as the 21st century was from King Minos of Crete. Time enough for human beings to learn how to travel faster than light, build settlements all around the galaxy and change themselves sometimes past the point of recognition. We've even met aliens at last, but they turned out to be so strange that little understanding was possible. So nowadays we mostly stay out of each other's way. The galaxy is large enough for that.
Where do I even begin to describe life in this era? People live in anything from vast, luxurious cities with kilometer-tall buildings to lost colonies that have reverted to preindustrial levels. Likewise, forms of government range from historical to outrageous experiments. Either way, the scales involved mean that polities seldom span more than a continent, let alone multiple star systems. And casual space travel makes it hard to keep people where they don't want to stay... or to find them again once they leave.
As a general rule, the closer you are to Earth, the more populous and developed the planets, while farther out technology and people alike become more exotic. Colonies, too, become more spaced out as you move away from the motherworld, reflecting the gradual increase in hyperdrive speeds over the ages.

Emigration

Either way, most people never leave the planet they were born on. After all, any of the older worlds provide enough opportunity for adventure to fill a lifetime. Or at least, what used to count as a lifetime. Space age medicine has lengthened the human lifespan so much that practically people no longer die of natural causes (unless of course they're kept away from proper treatment).
That means a world's population can grow faster than its ability to sustain life. Doubly so since most planets aren't as life-friendly as Earth, even with terraforming. And when that happens, finding a new planet to settle is a better long-term solution than building giant space stations for example, or hollowing asteroids -- though people do that as well.

War and trade

You see, thanks to hyperdrive it's not that much harder to reach a planet light years away compared to one in the same star system. And where there are distant locales, people will find reason to travel. Take trade, for example: in principle, most goods people need can be obtained in any star system, and a colony that can't provide all the basics for itself isn't worthy of the name. But there are exceptions to any rule. Antimatter can only be produced in expensive high-tech facilities not every polity can afford to build and operate. DNA samples are more useful in the form of living organisms than digital files. One-time encryption pads need to be shared via physical media to be useful, pretty much by definition.
And when trade can't get people what they want, they resort to war.
It's been said that all wars ultimately have an economic motivation, regardless of any ideological pretext. And sure enough, most wars in this age are local, for the reasons outlined above. But people aren't rational, and the first interstellar war happened as soon as there *were* extra-solar colonies to fight over. It was especially ruinous, wrecking the economies of entire planets for decades. Not that people ever learned...
Besides, in order to fight someone, you first have to find them in the vastness of the galaxy. And that's really hard if they're intent on hiding. There are simply too many stars to choose from.

Adventure

Ultimately, most people fly to the stars to get away. Away from an oppressive government, away from other people, away from routine... Out there you'll find rebels, people on sabbaticals, explorers poking at some yet-unexplored corner of space. It doesn't even have to be very far from home. And some people actually take their home with them around the galaxy.
Even so, going that far out is dangerous. Away from civilization, even minor health problems can turn into a disaster, not to mention failing machinery. So the people who go off into the void must be able to know more, do more and die hard. They have to be more than human.
We have a word for that, too.