Just a guess here, since not I'm not too sure on the specific terms, but a monsyllabic answers will have only one syllable (yes/no). You could answer 'uh-huh' for a positive response. What if the reply was 'maybe'? These are non-monsyllabic responses.
Possibly your brother was thinking of open and closed questions? Open questions need an answer thet goes beyond 'yes' or 'no'. Closed questions only require a 'yes/no' answer.
Probably someone else will be able to answer your question on the technical term for one word answers.
Not been of much help,