The facts of the case involved the police questioning of a suspect before arrest and before he was read his Miranda rights. The suspect refused to answer some questions, and the prosecutors in this case used his silence on that question in convicting him of murder, saying it helped demonstrate his guilt. The man appealed, stating that his Fifth Amendment right to stay silent should have kept lawyers from using his silence against him in court. Texas courts disagreed, saying pre-Miranda silence is not protected by the Constitution. The high court just upheld that decision.
A little background on the the Fifth Amendment: it protects Americans against forced self-incrimination, with the Supreme Court saying that prosecutors cannot comment on a defendant's refusal to testify at trial. The courts have expanded that right to answering questions in police custody, with police required to tell people under arrest they have a right to remain silent without it being used in court.
In this case, the prosecutors argued that because the suspect was answering some questions, and not invoking his right to silence, and because he wasn't under arrest and wasn't compelled to speak, his silence on the incriminating question doesn't get constitutional protection.
This is a very interesting case that will have a major impact on Michigan criminal cases going forward.