What is Admonition?

Legal Definition
Admonition (or "being admonished") is a punishment under Scots law when an offender has been found guilty but is neither imprisoned nor fined but receives verbal discipline and is afterwards set free; the conviction is still recorded. This disposition is comparable to an absolute discharge in jurisdictions where an absolute discharge involves the recording of a conviction (i.e., where the "discharge" is from punishment only) but stands in contrast to an absolute discharge in jurisdictions in which an absolute discharge does not involve the recording of a conviction (i.e., where the "discharge" is from conviction as well).

It is usually the result of either the strict application of law where no real wrong has been caused or where other circumstances (e.g. time already spent in custody or attending court) make further punishment unjust in the circumstances specific to the case involved.
-- Wikipedia
Legal Definition
A reprimamd from a judge to a person accused, on being discharged, warning him of the consequences of his conduct, and intimating to him, that should he be guilty of the same fault for which he has been admonished, he will be punished with greater severity. Merlin, Repert. h. t.

2. The admonition was authorized by the civil law, as a species of punishment for slight misdemeanors. Vide Reprimand
-- Bouviers Law Dictionary
Legal Definition
In ecclesiastical law, this is the lightest form of punishment, consisting in a reprimand and warning administered by the judge to the defendant. If the latter does not obey the admonition, he may be more severely punished, as by suspension, etc.
-- Black's Law Dictionary