I don't actually know how the interests are intended to work, but I can say that the key feature of Bluesky is feeds. (I know this isn't at all obvious.) Feeds are third-party created, for the most part, and essentially function as filters. So, for example, I follow a movies feed. Any post which includes the movie camera emoji, the word "filmsky", or a few other keywords is included in the movies feed. It makes it very easy to swipe over and see discussions of cinema.
That sounds (and is) a lot like tag-based feeds over on Twitter. However, there's additional potential. Behind the scenes, a feed is a service which takes the user info of the person viewing it and the firehose and decides which posts to include based on that input. So "include all posts with these keywords" is valid, but so is "include the top 100 posts with these keywords, as measured by likes." Or "show a feed including only the most recent post from every user the viewer follows."
In other words: feeds are the way a third party can build their own algorithm for the firehose. Very powerful, very useful.
That sounds (and is) a lot like tag-based feeds over on Twitter. However, there's additional potential. Behind the scenes, a feed is a service which takes the user info of the person viewing it and the firehose and decides which posts to include based on that input. So "include all posts with these keywords" is valid, but so is "include the top 100 posts with these keywords, as measured by likes." Or "show a feed including only the most recent post from every user the viewer follows."
In other words: feeds are the way a third party can build their own algorithm for the firehose. Very powerful, very useful.