"Miranda warning" refers to the constitutional requirement that once an individual is detained by the police, there are certain warnings a police officer is required to give to a detainee.
Miranda v. Arizona
The requirement to give Miranda warnings came from the Supreme Court decision, Miranda v. Arizona, 384 US 436 (1966). In Miranda, the Court held that a defendant cannot be questioned by police in the context of a custodial interrogation until the defendant is made aware of the right to remain silent, the right to consult with an attorney and have the attorney present during questioning, and the right to have an attorney appointed if indigent.
Fifth and Sixth Amendments
Without a Miranda warning or a valid waiver of the Miranda rights, statements made may be inadmissible at trial under the exclusionary rule, which prevents a party from using evidence at trial which had been gathered in violation of the United States Constitution.
For more on Miranda warnings, see this Southern Methodist University Law School article, this Pace Law Review article, and this Northwestern University Journal of Criminal Law & Criminology article.