A point in time at which a friend wants to go home and it is clearly before everyone else he or she is with is ready to end the fun. This term can be applied at any time of day.
It's 11:30PM on Saturday and everyone is out at a party.
Frank: "I'm kinda tired. I have to go home and study."
Adam: WHAT?!?! I didn't know it was BABY O'CLOCK!