Interestingly, in my edition of Black's Law Dictionary, the term "material witness" does not appear.

A more-recent edition defines the term, in two separate places. The two definitions are not entirely consistent, but have the same general thrust:

Material witness. A person who can give testimony no one else, or at least very few, can give. In an important criminal case, a material witness may sometimes be held by the government against his or her will. He may be the victim or an eye witness."

Witness [subhead: Material witness]. In criminal trial, a witness whose testimony is crucial to either the defense or prosecution. In most states, he may be required to furnish bond for his appearance and, for want of surety, he may be confined until he testifies.