An imp is a trouble maker — not a thug or a criminal, but a mischievous sort who might make prank phone calls or harass a substitute teacher.
Impe is an Old English word meaning young plant shoot. It was eventually applied to the offspring of people and later used pejoratively in the sense of offspring of the devil. The devilish meaning remains, but an imp can also be any mischievous person, especially a small child. You might call the boy you babysit an imp if he's in the habit of playing tricks on you — like locking you out of the house.