What difference does it make when there is a wire in the hood brim?

The brim mentioned here refers to the front edge that comes over the forehead when wearing the hood. In terms of a cap, it corresponds to the visor part sticking out in front. NYLON WINDBREAKER HOODED JACKET_PINK has a wire inserted inside this brim, making it possible for the wearer to shape the front silhouette into their desired form^[2].

If you bend it by hand, it stays that way. In general, unlike hoods made solely of fabric, a hood with a wire does not collapse on its own, so it is less likely to flip back in the wind or fall forward and block your view. You can also adjust and wear it according to the weather of the day, such as narrowing it closely to wrap around your face, or conversely spreading it wide to open up your view.

In terms of care, it is better to be careful about creasing. In general, if an area containing a wire is pressed hard or left bent for a long time, marks remain in that spot, and the shape can be distorted by the strong spin cycle of a washing machine or the heat of a dryer, so hand washing and air drying are safe. When storing it, it is also better to hang it on a clothes hanger so that the hood is not pressed down.

hmmm, that single line about inserting a core into the brim reads as a design that hands over the authority to determine the shape to the wearer, instead of dictating a finished shape.