This line is used for the exaggerateddescription of a dramatic turn of events in a moment of ones life.
"Nek minute" is often used in a way that leaves the end of the story open, meaning the listener is left to only presume what had happened, though it's not always used like this.
Also the person enlightening you with their wonderful story can replicate what happened themselves.
Can be also pronounced/spelled as "nek minnit", "neg minute"
Used instead of the phrase "Next Minute". No one knows its etymology (origin of word), except that it may have originated on the short-running TV3 show "The Jono Project". The phrase became extremely popular here in New Zealand and has been parodied many times since.
"Aww chur bro, makin' 2-minute noodles is easy as aye. Just boil some water, drop some noodles in there... Nek minnit... Hmm these noodles may need another minute aye..."
"I was talking to that weird girl Sharon, all was going fine, but nek minnit she hit me!"