I think we have to look at the meaning of "material" apart from the word "witness" to understand the term "material witness" properly. "Material" is used in legal documents and evidentiary law to mean the opposite of "immaterial". For instance, we often hear the expression "at all material times" meaning times which are relevant to the facts and issues in dispute or subject to examination. There is a latin expression which bears mention in this regard: de minimis non curat lex (or "de minimis" for short). Translation: "The law does not concern itself with trifles." A "material witness" is one who has more than trifling or "immaterial" evidence to present to the court.