admonition
A gentle warning or scolding meant to improve behavior.
An admonition is a warning or gentle scolding meant to guide someone away from trouble or toward better behavior. When a teacher gives you an admonition about talking too much in class, she's not yelling or punishing you, but she is making it clear that you need to change what you're doing. When a parent offers an admonition to be careful crossing the street, they're reminding you to stay alert and safe.
The word carries a sense of authority mixed with care. An admonition isn't mean-spirited: it comes from someone who wants to help you avoid a mistake or danger. A coach might give players an admonition about staying focused before a big game. A librarian might offer a quiet admonition to students getting too loud near the bookshelves.
The verb form is admonish. If your older sister admonishes you for leaving your bike in the driveway, she's warning you that someone might back over it. If a sign admonishes visitors to stay on the marked trail, it's a firm reminder to follow the rules. Admonitions work best when they're heeded because they give you a chance to correct course before facing real consequences.