(1) The substantial and basic fact or facts necessary to prove that a crime has been committed. (2) The material substance, such as the murdered body, on which a crime has been committed.
The police believed they had solved the crime, but they couldn't prove their case without the corpus delicti.
Corpus delicti literally means "body of the crime" in Latin. In its original sense the "body" in question refers not to a corpse but to the body of essential facts that taken together prove that a crime has been committed. In popular, nontechnical usage, corpus delicti also refers to the actual physical object upon which a crime has been committed. In case of arson, it would be a ruined building. In a murder case, as every fan of whodunits knows, it would be the victim's body.