The case is Manhattan Community Access Corp. v. Halleck, No. 17-702. Community Access Corp is a private operator of a public access television network. Halleck and another person were suspended by the Community Access Corp for expressing views that were critical of them.
Since social media outlets are arguably much more of a modern day public square than community access tv stations, a ruling for the plaintiff would certainly bring us closer to ridding ourselves of internet censorship that is violating our First Amendment right
More here. https://www.cnbc.com/2018/10/16/supreme-court-case-could-decide-fb-twitter-power-to-regulate-speech.html