Upvote:3
Those are typically worn to designate mourning in Western culture. However, its very rare to see them on anyone other than a man who has just or is just about to attend a funeral, usually as one of the pallbearers. Additionally, its only worn if the person in question doesn't have an appropriately black or dark suit coat (or dress) to wear, which is preferred.
Given that, if I saw someone in media depicted as wearing one, I'd think the writers wanted me to know that he'd recently gone to a funeral (or was on his way to one), without actually having to waste dialog explaining it to me.
Its basically a big flag that reads "someone died".