Understanding Collections first will make it easier to understand the Author Stories feature.
Typically, an author has a portfolio of stories they have written on your website over time. When readers read a story written by a certain author on your website, they can also access a list of other stories written by the same author, by clicking the Author's name that is displayed beside the story. This list is usually derived from an Automated Collection based on the Author's name.
The Author can maintain a curated list of their stories on your website, and have this list show up instead of the Automated Collection. Use the Author Stories feature to maintain this curated list. The list of stories can be customized using the various features available under Collections.
For example, you can have a Manual Collection with hand-picked stories featuring the top three in the Collection. Now, every time a reader selects the author's name beside the story - this customized list of stories written by the author will be displayed.