I understand it this way. Say, you are a nuclear terrorist and store atomic bomb schematics in S3. The FBI learns about that and tells Bezos (or whoever is Amazon CEO these days) to delete your files or go to jail. Bezos obliges. That's the centralized service.

Now if you store your atomic bomb schematics in Storj, FBI can't delete it because it's distributed across thousands of computers whose owners don't even know what they are storing.