An inquest refers to a formal legal analysis that is called in order to answer a question that needs to be answered so that a judicial proceeding to continue. Typically, an inquest is asked for when a person's death is unexplained and/or sudden.
In the United States, inquests are typically asked for by the courts and are carried out by coroners. Coroners are people who professionally determine causes of death. They are generally employees of the state. Inquests are almost always asked for in criminal cases in order to help determine a person's cause of death. The coroner's opinion is then used as evidence in the case. The jury will then decide, based on the coroner's opinion, the cause of death.