If you are among the 73% of American adults who don’t log in to Twitter at least once a month, you can be forgiven for viewing it primarily as a place where presidential candidates launch broadsides and celebrities embarrass themselves.

Twitter Inc.’s long struggle to define itself goes hand in hand with its recent inability to grow beyond its active but hard to grasp subcommunities. The mix of content, curation, humor, self-promotion and invective confounds its product teams, leaders and investors.

So...