For me, the prime example of this is Outer Wilds. However, it applies to other similar games. In the game, the player explores a solar system. This has the following implications:
- We have a huge space to explore.
- There are planets are moving all the time anyway.
Since everything is moving anyway, then moving everything instead of moving the player character is not really an extra cost.
And why would you want to move everything instead of moving the player character? Because floating point precision.
For a good example of the problems that floating point precision brings, let us see a game with huge worlds that does not do this: Minecraft. See THE TRUE END of the MINECRAFT WORLD!.
As you move away form the origin you will start to see problems.
This is because floating point numbers can represent more values near zero than away from zero.
In case you are not familiar with how floating point numbers work, first of all, here are a couple videos: Why Computers are Bad at Algebra | Infinite Series and Floating Point Numbers - Computerphile.
However, for the purposes of this answer, you can think of them as a scientific notation (with a mantissa and an exponent), or you can think of it as moving the decimal point (hence the name). These are the same idea: As the exponent becomes larger, you are moving the decimal point to the right, so that there are less digits after it.
Thus, the first symptom is that motion becomes jittery. This is because the difference between a floating point number value and the next becomes large enough that it is noticeable. Thanks to rounding, motion is still posible, but not smooth.
Eventually there there are no digits after the decimal point. And then you keep moving the decimal point (i.e. increasing the exponent), and the floating point numbers begin to skip integers altogether. When you reach those values we have another interesting behavior: a floating number value plus one is the same floating number value. Because the next integer cannot be represented as a floating point number, and is rounded down.
I remind you that the gap between values that can be represented becomes larger and larger. So for any gap you can think of, there will be a position where the gap between values that can be represented is larger… Well, eventually you reach the larger number that can be represented, and that is that.
What I'm going with this is this: eventually the distance that the player character would move is too small to make the gap between values that can be represented, and then the character can't keep moving.
And, of course, for any other system that depends on the position in your game (e.g. motion, models, lighting and shadows, world generation, etc) the progressive lose of precision as you move away from the origin will introduce weirder and weirder behavior.
To avoid all that you want to keep the player character near the origin. And that would mean to move the world.