Mischief is reckless or malicious behavior (such as playing pranks) that deliberately causes harm, damage, or annoyance in others. It can also mean a tendency to cause embarrassment.
Mischievous means more or less the same as naughty or badly behaved. Children are often punished in some way when they act mischievous.
The etymology of the word comes from Old French meschief, which means "misfortune,' from meschever, "to end badly."
Mischief in criminal law
In criminal law, the term mischief is used for vandalism, graffiti, or some other destruction or defacement of property.