Someone who's scholarly is a serious student. You can describe your studious friend who's always working on a research paper or reading a huge book as scholarly.
Use the adjective scholarly when you talk about a person who is focused on learning — in other words, a scholar. You can also describe things that relate to studying or knowledge as scholarly, like a scholarly article in a journal or a scholarly atmosphere in a library. The Old English word scolere, or "student," is the root of both scholar and scholarly, from the Latin word for school, schola.