This is the adjective for entomology — the science that studies insects. An entomological journal is a magazine about that science; entomological research is research on insects; an entomological collection is a set of insects kept for study. Scientists, museums, and universities use it. You will almost never hear it in a shop or on the bus. Though actually it does not mean “about insects” in a loose everyday way (you would just say insect there). It means “about the scientific study of insects.”