Miranda v. Arizona, 384 US 436 (1966)
Miranda applied the "exclusionary rule" to any statements or confessions the defendant made in response to police interrogation if the defendant hadn't been informed of relevant due process rights beforehand. Under the exclusionary rule, illegally obtained evidence may not be used to convict a defendant in court.
According to the US Supreme Court, a person in police custody must be told he (or she) has the right to remain silent to avoid self-incrimination (Fifth Amendment). The person must also be advised of the right to have an attorney present before and during questioning, and to receive court-appointed legal counsel if he (she) can't afford to hire an attorney (Sixth Amendment).
The decision in Miranda wisely assumes ignorance of constitutional rights. If the person in custody is not advised of these rights, and doesn't invoke the rights, any exculpatory or inculpatory statements are considered unconstitutionally obtained evidence, and are inadmissible in court.
The Miranda ruling has been revised somewhat by subsequent Supreme Court decisions. On June 1, 2010, the Roberts' Court released the opinion for Berghuis v. Thompkins, 08-1470 (2010), which held a defendant must invoke his right to remain silent (by stating he wants to remain silent), rather than waive it (by explicitly agreeing to answer questions before interrogation).