There is a possibility that apron came to apply to boxes because of the French cavalry timpanists, called timbaliers. In the 18th c., as aprons were part of their standard equipment.
Since a timpani is not exactly the easiest instrument to carry around (let alone two of them, on horse back, on the battlefield), they were placed in wicker baskets. The sides of those baskets were decorated with cloth, often embroidered with coat of arms.
That’s probably why you haven’t heard the term apron to designate, well, the side of a game box. The term is mostly used by collectors, as antique or hand crafted game boxes often have their sides covered with decorative cloth or paper.
As for modern game boxes, they don’t “wear” aprons anymore. They’re rather wrapped in a film, glued in the factory. It is called the box wrap.
Antique or modern, game boxes are often victims of a condition called split aprons, where two or more aprons become detached along the box edges. This often results in dishing. Split aprons can be repaired in different ways.
The aprons or sides of a typical game box are not called flaps or folds. Very few board game boxes have actual folds — a notable exception being the well-known Crimson Container, a.k.a. the “pizza box”, used by Victory Point Games.
The term apron is rare, but not what it means. You’ve seen hundreds of aprons as soon as you’ve watched a few minutes of board game reviews on YouTube. There seems to be a consensus that they make for the best background.
Which is debatable. Walls of games can become samey and boring. In some cases however, it can be a welcome distraction.
References and Further Browsing
- Apron, on The Big Game Hunter
- Repairing split aprons, on The Games Journal
- Repairing split aprons (2), on The Games Journal