It's a reference to one of the most culturally important stories in Buddhist countries. Not knowing about it is like consuming English media without knowing anything about Shakespeare's plays.
The English name is Journey to the West and the monkey is Sun Wukong in Chinese or Son Goku in Japanese. You might notice the main character in Dragon Ball Z has the same name, but the monkey king is referenced constantly in all sorts of Eastern media. The synopsis and main characters sections in that Wikipedia link will give you the general idea, but I would recommend reading or watching any of the versions to get a better understanding of the vibe.
Your metaphor is basically just calling them arrogant and reckless, lacking a good strategy and rushing in to things.