Silliness or fooling around; dishonest or illegal activities; idiotic pranks.
Bubba was sent to the principal's office for monkey business - he used a monkey instead of an apple to greet the new teacher.
This expression has two meanings. One concerns comical behaviour like that of a playful monkey. The other refers to sneaky, unlawful actions. So a student could be sent to the principal’s office for monkey business and a politician can be sent to jail for monkey business.
This idiom, from 20th century America, is like many other expressions that relate human behavior and animal behavior (sly as a fox and wise as an owl), and probably comes from an older expression, monkeyshines which dates from the 1820s.