When an officer places you under arrest, you will hear about your rights. One of those is the right to remain silent. This is a very important right you have to protect yourself.
Findlaw explains the right to remain silent means you do not have to provide information or answer questions from officers. You never have to tell them anything except your name.
One of the reasons why you have this right is because the US Constitution guarantees you that you do not have to testify against yourself. Speaking to an officer will provide information that the prosecution could then later use against you in court. It would essentially be like you testifying in the courtroom.
Maintaining your right to stay silent is important because it will help you not give evidence against yourself. It enables you to speak with an attorney first and begin mounting a defense before the prosecutor can even file charges.
The right to remain silent means you do not have to answer questions or give officers any information beyond your name. Do note that if you do provide information, it must be truthful. You should never give a false name because you can get into trouble for lying to a member of law enforcement.
Also, keep in mind that officers know about this right but may continue to try to get you to talk. You should state clearly that you wish to invoke your right to stay silent. Also, evoke your right to an attorney. Any information officers gather after you make it clear you do not want to talk may be easy to get a court to throw out if you can show they coerced it out of you. However, that does not mean you should start talking. Stay silent and do not engage with officers regardless of what they may say or do.