Twitter and other social networks have agreed to delete individual posts, but that's not considered good enough. BirGun is defying the censorship, and the court believes that the media outlet is interfering with both the investigation and national security as a whole.
Twitter hasn't said precisely how it'll respond, although the company tells the New York Times that it'll "work diligently" to keep its service available to Turkish residents while protecting their rights. Turkey's officials have been looking for reasons to drop the hammer on Twitter, and it's hard to see that paper's account remaining accessible without some severe consequences.