Definition
Hazy, uncertain, or imprecise. Used in reference to words — especially sentences and paragraphs — that are not clearly expressed. A criminal statute is void for vagueness if it is so vague that it fails to give a person fair notice of what conduct is prohibited or required. A statute is also void for vagueness if a legislature's delegation of authority to judges and/or administrators is so extensive that it would lead to arbitrary prosecutions.
Illustrative caselaw
See, e.g. Skilling v. United States, 130 S.Ct. 2896 (2010).