According to Merriam-Webster the definition for the word "admonition" is a "gentle or friendly reproof". This is stated as the word's primary definition. Its secondary definition according to this dictionary is "counsel or warning against fault or oversight".
Therefore, someone is "admonished" by someone else in order to correct and/or warn the individual about a certain course of action that the admonishing party believes is not appropriate or right.
An admonition is a way to gently warn someone that they should heed the advice that will help them avoid unpleasant results due to their wrong actions. An "admonition" is a way to forewarn someone that continued actions may harm them and/or others. It is a way to get an individual to see that they're on a faulty course that needs correcting to a right course.
Admonition is defined as a mild, kind, yet earnest reproof. It is also defined as cautionary advice or warning.