To chasten someone is to correct him or her, often with the use of some pretty steep punishment. Chasten can also mean "to restrain." Either of these actions may be necessary when someone isn't behaving like they're supposed to.
The verb chasten is often used with the verb "to be" as in "be chastened." If students are caught writing graffiti on the bathroom wall, you can expect them to "be chastened" by both the school and their parents. Chasten is related to the word chastise, meaning "to punish severely." Both words can be traced back to the Latin root castus, meaning "morally pure." So keep yourself on the straight and narrow when it comes to morality and you can avoid being chastened.