A cheese monkey is a monkey with cheese, or a cheese coloured (or yellow) monkey. A monkey eating cheese is a very rare site to see in some cases so this is why people use this term.
Person 1: "Hey look at that!'
Person 2: "What?"
Person 1: "It's a monkey eating cheese!"
Person 2: "Oh a Cheese Monkey?"
Person 1: "Yeah I guess"
Term often used to describe a random, pointless act or outburst. Commonly used in an attempt to draw hilarity where none is found. Family Guy is notorious for many acts of 'monkey cheese' in its various flashbacks to scenes which have little or nothing to do with the plot, but are totally random in an attempt to draw a laugh.
zomg random ninja explosions! pirates robots woot thats some monkey cheese shit right there!!! z0r :awesome:
The second episode of Shit Pickle (by James Rolfe aka AVGN) introduces a family of monkeys who just like to repeat the phrase "Monkey cheese". This is just some random phrase meaning nothing.