For example, the prosecutor in a criminal court might argue how bad the crime is that has been committed, but if this argument is taken as an argument to convict the suspect, it is a case of ignoratio elenchi--it does not prove what it should prove, namely that the suspect is the one who committed it.
Aristotle believed that an ignoratio elenchi is a mistake made by a questioner while attempting to refute a respondent's argument. He called it an ignorance of what makes for a refutation.