Misinterpretation is a case of misunderstanding something or (interpreting it incorrectly). Singing "Will you still feed me when I'm six feet four?" is a misinterpretation of the Beatles song "When I'm Sixty-Four."
Interpretation comes from the Latin interpretari, which means "explain" or "translate." Adding the prefix mis- (which in this case means "wrongly") changes the word's meaning to "wrong interpretation." Misinterpretation is often accidental, but it can be intentional, too. "Willful misinterpretation" is misunderstanding someone else's words on purpose, often to make an unrelated point.