One story about the origin of this phrase is that it comes from when Primeminister Lord Robert Salisbury appointed Arthur Balfour, his nephew, to the post of Secretary for Ireland in 1887. Young Art was not really all that deserving and only got the post (an important one) as a result of his uncle. Hence, the phrase.

Most common use would be at the end of explaining how to do something . . . "you just stick this in here, twist that, pull on this and, hey, Bob's your uncle, you're done"

. . . . actually, on second thoughts, that sounds vaguely obscene.