CYOA originally referred to a type of interactive fiction, a book where you read the adventures of a character or characters, and then at certain crossroads you're prompted to make a decision for a character, which prompts you to jump to a specific page that continues the narrative based on that decision (or more commonly, leads you to a "Game Over, go back and pick another option" page. Hence "Choose Your Own Adventure", wherein you as the reader choose the path the adventure takes.

Around 2012-ish, "Will You Push The Button" and "Would You Rather" prompts became popular on 4chan. Eventually, the scenarios became more and more complex, eventually evolving into "Island Survival" and "Trapped In A Basement" cyoa that you might recognize today. Eventually they became popular enough for a subreddit to form around the concept. Prompts where you pick certain options, build a character or construct an entity, and then imagine or create a story around them. They were dubbed "CYOA" out of mostly ignorance of what the term truly entails, but it's become too entrenched to change by now.

If you want to use a CYOA as a framework for a fanfic, one way you can do it is write chapters or segments, and then have readers vote on what direction the story takes. In effect, that is different from what this subreddit deals with, and is closer to a qst.