To express disbelief or skepticism at an idea, or surprise when you find something unexpected to be true.
If Paul Martin remains in office, I'll be a monkey's uncle.
The publication of Darwin's theory of evolution in the Decent of Man was greeted with derision and a great deal of skepticism. The idea that man is related by a common ancestor to apes and monkeys was considered the most outrageous of the claims.
I'll be a monkey's uncle was originally a sarcastic remark by a non-believer of Darwin's theory and was intended to ridicule the theory of evolution.