It means target people with needs that aren't being met. Those people are not consuming (i.e. buying and using) a product or service to address their problem.
It's clearest to see when a product exists to solve a problem, but it's too expensive for some people (or some situation). In the article, the problem of reporting on local sports/financials has a solution (reporters), but the value of that news isn't worth their time: their time is too expensive. So the newspaper doesn't "consume" a solution to the problem of reporting that particular news.
By targeting this non-consumption, the startup doesn't compete against reporters (yet...), so it provokes no desperate fight for survival.
It's an term from Clayton Christensen, who wrote The Innovator's Dilemma, though he doesn't use it til "The Innovator's Solution", and expands on it in "Seeing What's Next".
