it's not so much a proverb as a saying that people use sometimes when they have, for example, demonstrated something. Let's say they showed you how to make scrambled eggs, they may get to the final bit and say "Bob's your uncle - you now have scrambled eggs". I don't think there is agreement on how this saying originated.
I can't remember the exact details from my History lessons years ago. It comes from a British politician who gave one of his relatives a job-- inferring nepotism rather equality of opportunity.