A nonversation is simply a conversation with someone who you do not wish to talk with, therefore using as many one word answers as possible, hoping that they get the hint.
Librarian: So hav you read many books this year?
Librarian: Oh...did you at least finish that book set for your school project?
Librarian: Did it take you long?
Schoolboy: about a week......i gtg (runs really fast in opposite direction)
Schoolboy: Man...that was the worst nonversation i evr had!
Friend: Really i find the librarian really nice to talk with
(all other kids stare)