Last night I read Flickr's patent on its interestingness algorithm. Patents are not easy to decipher sometimes, especially if they're written well as this one is, but I think I have some interesting things to share...
(Note: Please don't confuse the following with a discussion about Explore. Explore depends on interestingness, but getting into Explore depends on a lot more than just interestingness.)
From reading the patent, it seems to me that the entire "Flickr System" is largely built around this notion of interestingness, so anyone who says that popularity and interestingness are not important in Flickr universe is dead wrong. My intuition is that Flickr was designed first as a means to provide superior search results to seekers of "media objects", and second as a social network. It's interesting to see that the patent description forsees video and other objects, as well as launched advertising specific to the content of the media object (i.e. image).
The basics of the "interestingness score" that Flickr calculates for each of your images have been discussed here and many places: how many faves, comments, notes, views, and where the views come from (e.g. an award group versus an outside search engine). Also discussed elsewhere is the "how many groups" question (answer: 1-5 good, +5 perhaps penalized).
Here are some tidbits from the patent that perhaps are less
--Interestingness is affected by how long it's been since your last upload (it doesn't say how it takes any of these factors into account by the way!)
--The EXIF camera data is important to have. If you are uploading scanned images (e.g. film) it likely won't have such data. My recent lomos didn't get into Explore until I added the EXIF data (I use a Mac, so I used some freeware called "Reveal 1.2").
--Other metadata is important to have. I haven't done "controlled experiments" on this, but my guess if the title, description, tags, or sets are empty, that decreases interestingness.
--Interestingness is decremented over time (e.g. 2% a day); and is decremented in the presence of metadata (in the title, text, tags, comments, notes) of blacklisted words (you can guess what those are!)
I also found it interesting that an image's interestingness score can be customized to the requester of the score. For example, if you've faved a lot of my pics with a particular tag, then other pics that you haven't faved but which have the same tag will show up to you as "more interesting".
Of course, in the end, faves and views and comments and all that stuff is the outcome--the cause is having an interesting photo to start with!
The information above is still correct, although I think the underlying Interestingness has become more complex than when I posted this 7 years ago. In general, a photo will be more interesting with more faves and comments, and text in the title, description, and tags, and EXIF and geo-tagging metadata.
There's an apparent moderate tradeoff between Interestingness and Relevance within the Flickr search engine. Fewer words in title, description, and tags usually increases Relevance but decreases Interestingness.
Optimize for Interestingness is you want to get into Explore, and show up high in the Interesting tab in Flickr Search. Optimize for Relevance if you want to show up high in the Relevant tab in Flickr Search. Note that all Flickr searches default to Relevant, so ceteris paribus this is a better tab to be ranked high in.