In the context of mobile apps, story interactions is the overall engagement that you get from your users from all content that is uploaded on social media app stories. In the modern-day world, a lot of business, marketing campaigns, promotional offers and product awareness is based on what users see on their social media app stories like Instagram, Facebook, etc.
All the clicks, impressions or other desired actions that you get on these stories is counted as a story interaction. This could include taps on location, hashtags, mentions, URLs, etc. Stories analytics has become quite a useful metric while assessing the overall success of failure of an ad campaign in the digital scheme of things.