admonish
To firmly warn someone so they will do better.
To admonish someone means to firmly warn or scold them about something they did wrong, usually to prevent them from making the same mistake again. When your teacher admonishes you for talking during a lesson, she's pointing out that your behavior disrupts the class and needs to change, with the expectation that you'll correct it.
An admonishment carries a tone of authority and seriousness. A parent might admonish a child for running into the street without looking, because the danger is real. A coach might admonish players for not following the game plan. The word suggests the person giving the warning genuinely cares about preventing problems or helping someone improve.
Admonishing is different from casual reminders or gentle suggestions. It's firmer than that, with real concern behind it. But it's also different from harsh punishment or angry yelling. When someone admonishes you, they're taking you seriously enough to correct you directly, expecting you to understand and do better.