I've written a few past answers on folk dress that are a very helpful background for this:
Why are countries' traditional costumes usually from the 1800s?
Why doesn't England have an official national dress?
More on Norwegian folk dress specifically
As you can see from these, most European folk dress is a semi-crystallized form of what actual peasants were wearing in the late 18th-19th centuries, often in a cleaned-up, generalized, and/or deliberately designed style. And at that time, a lot of women were wearing aprons. Why?
Aprons were actually worn by women up and down the social scale in the eighteenth century. At its most basic, the accessory was obviously something used to protect the clothing from whatever its wearer was working with - dough, fruit juices, sawdust, animal hair, etc. - as well as a piece of fabric that could be used for wiping one's hands or, by holding up the lower end, creating a kind of basket. Highly useful! But for women who weren't really doing anything that could hurt their clothing or get their hands dirty, it was also a space for display of needlework and fine fabrics. For instance, this early eighteenth century example is embroidered with brightly-colored silks; when worn, it would have looked something like the one shown in this portrait of the Strong family. By the middle of the century, they were more typically longer, white, and sheer; if they were embroidered, it was generally with white thread, as seen in this portrait of the daughters of the Earl of Bute. I would argue that it had such staying power as a part of fashion even when unnecessary because it was a symbol of or callback to the housewifely role that all women were supposed to aspire to - it was a way for them to perform virtue/femininity.
For folk dress imitating eighteenth-century styles, many of the same considerations apply. The apron as part of a festival costume worn by middle-class women calls back to the time when this type of clothing was only worn by workers, when the apron was functional. It also becomes a site for embroidery and other embellishments in patterns that signal national identity.