A monkey is a tropical, long-tailed animal known as a "primate." If you visit India or Sri Lanka, you're almost guaranteed to see monkeys, but don't monkey around with them.
Many monkeys live in trees, although some are ground-dwelling, and increasingly many live in urban areas, scavenging food and interacting with people. Monkeys are famously playful and mischievous, and because of this, monkey is a common diminutive (or fond nickname) for impish kids, and "monkey business" is foolishness or deceitful behavior. When you monkey around, or monkey with something, you fool about or fiddle with it.