Bringing a skateboard to school is a great way to get an admonition from a teacher not to ride it down the halls. An admonition is advice with a hint of scolding, a warning not to do something.
When you're cautioned or warned about some mistake you might be just about to make, or some looming danger, you're receiving an admonition. The strength and tone of an admonition determine whether it's a gentle, polite suggestion or more of a stern warning. In Scotland, an admonition is an official legal term that means a verbal punishment for someone who's been found guilty but set free.