The Miranda warning is a required reading of the constitutional rights a suspect has by the police while the suspect is held in their custody, before the police may question him.
There are public safety and national security exemptions to the requirement of providing the Miranda warning. In the arrest of the 19-year-old Boston Marathon bombing suspect, law enforcement invoked the public safety exemption in choosing not to provide the Miranda warning to the suspect.
Outlined in the Fifth and Sixth Amendments - The right to remain silent, that anything he says will be used against him in court, right to have an attorney present during questioning, an attorney will be appointed if the person cannot afford one. The police will then ask if the suspect understands this warning.
Its name is from the leading case, Miranda v. Arizona.