In the English-speaking world, it's often used to mean playing around in a non-serious way, like in the expression "monkeying around." It can also be used self-deprecatingly to describe foolish or childish behavior.

In Eastern cultures, thanks to Sun Wukong from "Journey to the West," the monkey is known as a clever but cunning character. So, it's not just used for playful behavior, but also wittily to show off outstanding cleverness or talent.