Just that. An absolute right to say nothing if a person is in custody and is being questioned by police. It is in your best interest to invoke that right and say nothing until you have a criminal defense attorney present. The police may legally use various tactics in this setting in an attempt to get a suspect to admit to a crime or make incriminating statements. These tactics may include appealing to a person’s guilt or conscience, engaging in ploys like ‘good-cop/bad-cop’, lying about the evidence against the person, making promises of leniency or release if the suspect confesses to a crime, or outright intimidation. This is such an inherently coercive setting for a person that the U.S. Supreme Court ordered that the now-famous Miranda warnings be read to a person before the questioning process begins. You have the right to remain silent. Everything you say will be used against you. You have the right to a lawyer. If you cannot afford a lawyer, one will be appointed to you.
Despite the warnings, people often ignore these rights and give incriminating statements to police that they later say are false, inaccurate, or the result of abuse, coercion or intimidation. Also, people often forget that any communication or information given to police is a statement – not just a written and signed statement. These statements will be used against a person – just like the warning says.
An analogy: If you have a baseball bat, and someone tells you that if you hand him the bat he will hit you over the head with it, would you give that person the bat?
Think about the right to remain silent the same way – say nothing and ask for a lawyer.