Q. What is a monograph?

You can think of the word monograph as a fancy way of saying book. It is usually a longer written work about one particular topic. It comes from the Greek words mono meaning "one or single", and graph meaning "something written". See the etymology here: https://www.etymonline.com/word/monograph

When your professor asks you to use monographs as sources for your paper, they want you to find and read books on the topic.