Do something punctually and you do it at exactly the right time — not a moment too late. If your teacher expects you to arrive punctually, you'd better get to class before the bell rings!
People who are always on time are known for doing things punctually. Arriving punctually at the airport means you'll never miss a flight. Finishing your book report punctually means you'll hand it in before the deadline. The adverb punctually comes from punctual and its Latin root punctus, "a pricking." In fact, punctual originally meant "having a sharp point," and evolved to "insisting on fine points" or "prompt."