they come from a time when FTP was a thing, upload bandwidth wasn't cheap and Steam/Youtube/.. just weren't. Want people to download your game demo or your video? Better pay.
So some CompSci people sat down and looked at how to copy/distribute data better and described distributed networks and someone implemented these thoughts into "torrent" (there are others). IIRC at the same time we were at the height of the music piracy discussion (before Itunes, I think?) and torrent slotted into the role of "a faster Napster, also movies!".
Since the advent of cheaper bandwidth the need isn't quite there anymore and I have only used it for DVDs of Linux distributions (which ironically has always been unnecessary as universities provide mirrors and they just have bandwidth).