The phrase that someone "turned himself in for the crime" is one that is commonly heard in local TV news and movies, but doesn't always have a specific meaning. At the very least, it refers to a person presenting himself to the police or other authorities for arrest and/or to say he committed a crime. There can be good reasons for doing this, and some decidedly very bad reasons for doing which can bring disastrous consequences. You should always speak with an experienced criminal defense attorney in your jurisdiction before taking any action to present yourself and/or evidence of a crime that you may have committed to law enforcement authorities.
Near the beginning of any formal criminal proceeding, the charged defendant has the option of pleading guilty or not guilty. For some people, the idea of ever pleading guilty to a crime makes no sense. Others may be motivated to plead guilty for a variety of reasons, not the least of which is the knowledge that they did in fact commit the crime with which they are charged.
Many people who are facing arrest and/or investigation for a state or federal crime wonder how much they should tell their criminal defense attorney about what actually happened, for fear of endangering themselves, their family, or others who could be implicated in the crime. This could involve a hundred different topics about a hundred different aspects of a potential crime, but this often comes down to a simple question: should I tell my lawyer if I (or another person) actually committed the crime?