Dough mixed the night before rolls out noticeably better than dough mixed twenty minutes ago. Two separate processes are running during that rest, and both help.
Bran takes a long time to absorb water
Whole wheat flour contains bran particles that hydrate far more slowly than the starchy endosperm around them. Fresh dough has water distributed unevenly between the two.
Until the bran is saturated it keeps drawing moisture from the dough, which is why a bowl that felt right at mixing can feel stiff an hour later.
A long rest evens this out. The dough that comes out of the refrigerator is uniformly hydrated, which is what makes it roll smoothly rather than in patches.
Gluten relaxes when it is left alone
Kneading aligns and tensions gluten strands, and a tensioned dough springs back as fast as it is rolled. Resting lets those bonds rearrange into a slack state.
A relaxed dough rolls thinner for the same effort and holds the shape it is given, which matters because an even thickness is what allows a flatbread to inflate.
The bran also does damage here, since sharp particles cut gluten strands. Extra hydration time partly offsets that by making the bran softer and less abrasive.
Cold slows the changes you do not want
At room temperature a wet flour dough starts fermenting from the microbes already present, and after several hours it sours and turns sticky.
Refrigeration slows that to a crawl while hydration continues, which is the whole reason the rest happens cold rather than on the counter.
Dough kept longer than a couple of days will still develop off flavors and gray at the surface, so the technique buys days rather than a week.
Handling it out of the refrigerator
Cold dough is firm and resists rolling, so most cooks let a portion sit out while the pan heats. Ten or fifteen minutes is usually enough.
A brief knead redistributes any surface moisture that has condensed and restores an even texture, without rebuilding the tension that resting removed.
The dough will also feel wetter than it did at mixing, because the bran has finished absorbing and released its grip on the surface, so extra flour is rarely needed.
What this buys a weekday kitchen
Mixing dough is the slow, messy part, and rolling and cooking is the fast part. Separating them moves the effort to whenever there is time.
Dough also keeps better than cooked flatbread, which stales within hours. Storing the raw material rather than the finished product gives a better result at the same convenience.
Portioning into balls before chilling shortens the weekday step further, though each ball needs covering, since exposed surfaces dry into a skin that will not roll out cleanly.