Short for "Nibble". A response or retaliation by an individual when you are directly trying to irritate them to get a reply. The individual nibbles at the "bait" you have laid out (the insult or statement directed at them, which you know they will respond to), at which point you say "Nibs", which further evokes a response.
George: "You're shit at this game mate, you said you were decent"
Sam: "Fuck off no I'm not, I'm still better than you"
George: "Nibs"
Mock title (such as your majesty) used to refer to an authoritative, bossy or demanding person. It could be a grown up or a child acting like a spoiled brat. For a female you may use Her Nibs.
"His Nibs is demanding his coffee immediately" - when a boss decides that he has to send out someone to get his coffee because he is just "too busy" to get it himself