The hour of the night past the witching hour, which begins at 4:00 AM. Most commonly used in Michigan and Chicago to refer to that time of the night when shit gets weird.
"Dude... what the hell was that?"
"I don't know, it's the didly hour, shit gets wierd."
the level at which an act or phrase becomes beyond the want of human comprehension. A friend of mine went "all in" in a texas hold em pokergame with a pair of 2's for no apparent reason.