Popularity is an outcome. It may arise due to a combination of features (e.g. adding viral 'share this' buttons, or having karma to encourage participation from existing users) but it's not a feature in the sense of 'a piece of functionality you can build'.

It's an important outcome, and the OP will need to figure out what features will encourage/support popularity.

Hacker News's list of features is, let's be honest, spartan. Yet it still manages to pull in considerable viewership precisely because it's popular. Circular reasoning, I know. That's the way it works.

Popularity isn't just a feature - it's the single most important feature in any community-driven website.