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!"