I don't claim to be expert in the science involved here. (But then, there really is no true "science" here, as we don't have any examples of such a world available to study. There can only be speculation and extrapolation based on science.)
Assuming one side of the world always faces the sun and the other side always faces away:
Most plants as we know them could not survive on the night side, as they would never get sunlight to power photosynthesis. That would make it tough for animals to live either, as they wouldn't have plants to eat to make a foundation for the food chain. Presumably animals living near the boundary could travel back and forth.
Presumably the day side would get much hotter than the night side. But if the night side is mostly dead anyway, that's not much of a direct problem from a world-building point of view: You just posit distance from the sun, atmospheric composition et al sufficient to make the day side a reasonable temperature for life. Then the dark side is very cold. How much colder depends on thickness of the atmosphere, weather patters, whether there are moons, etc.
The hotter day side would mean that air gets heated and expands, and then must move toward the dark side where it cools. Of course air can't continually flow from light to dark so there must be currents bringing it back. In short, I think you have some pretty constant high winds.
Similarly with ocean currents. I think the surface will tend to be moving dark-ward while there's an undercurrent flowing light-ward.
If the people basically live on the light side, the dark side is a barren, unknown, mysterious land. In early days a few brave souls probably venture there. As technology advances eventually they reach the point where they can launch serious expeditions and truly colonize the place.
Another scenario may be for the planet to be in a system with multiple suns, so that all or most of the surface is getting light from at least one of the suns at any given time.
(Isaac Asimov wrote a story about such a world many years ago called "Nightfall", where it is only night for one day every thousand years or some such, and when that day comes people go insane. It was a well-written, entertaining story, but it seemed to me to have a lot of plot holes. Like, given the whole multiple-star premise, any particular spot on the planet might have night only on these rare occasions, when it happens that given the dynamics of the system, that part of the planet is facing away from all the stars, and/or they are eclipsed by moons. But the whole planet wouldn't go dark at the same time, it would be one piece here, one piece there. So even if we accepted that the darkness drives people insane, it wouldn't be the whole planet at once, just part of it, so it's not clear why civilization would collapse. And why would darkness drive people insane? Even if it's never night, people don't normally go insane because they experience a previously unknown natural phenomenon. I didn't go insane the first time I saw a tornado. And even without night, don't people on this planet have caves, windowless basements, shipping boxes, etc, that they would experience darkness now and then? Oh well, whatever.)
Anyway, if multiple stars were close enough that a planet would receive daylight-level sun from several of them, would such a system be stable? I'm sure someone's worked out the physics of that to say if it's possible.