It's a way to decide who has to do something you obviously don't want to do. These are the rules: someone calls "No nose goes" and the last person who touches his or her nose or whoever doesn't touch it at all is left with the task everyone else just avoided (hence NO nose goes).
The game is not "nose goes," although that is an option for the game. "Nose goes" indicates that touching your nose means you go, which is exactly what you are trying to avoid. This is another version for experienced no nose goes-ers where the over-ambitious are the first to touch their nose and then lose.