The author updates, usually on a schedule of the same day every week or every other week and the most recent bit is appended to the previous part automagically and appears on the Kindle. I'm currently reading one called "Ex on the Beach" by Kim Law, so-so storyline, so-so writing, but I had a lot on a giftcard so I bought it.
ETA: Curious thing, is at the end there is a link to an
Amazon discussion forum for the single. Interactive writing at its best (and worst), methinks.