Any communication contains explicit and implicit parts, the ones said/written and ones meant, but not passed literally.
In the example the speaker implies the subject should not misbehave with their parents.
This is pretty general but then it conveys the essence - to imply something is exactly the activity of conveying something without saying it, but the noun - Implication has broader meaning, so that won't quite do as the name of the activity.
There is also Innuendo but that's an entirely different way of conveying hidden meaning - the speech is about seemingly entirely unrelated subject and only by following the flow of metaphors you reach the hidden meaning - not what happens here.
And of course in the end there's the plain meaning. The speaker meant to stop the subject from misbehaving by parents. It doesn't exactly follow the "implicit" line - if you say "could you pass the salt please" you mean you want to have the salt passed to you, no hidden motives.