It's a way to end a conversation you started. Only you can zitto (end) a conversation which you stated and no body else. Same holds true for the conversations started by others. You can't zitto other peoples conversation.
Herman: hey Reena ... who do you like the most "your boy friend or me"
Reena: you cutie pie .. no doubts on that. Who do you like the most "me or your girl friend"
Herman: ummmm .... zitto
Reena: Damn it!