This gesture, typically seen in fiction such as anime, manga, rather old films or dramas, and typically done by young boys, indicates one's pride, confidence, and/or Shyness.
Sometimes a similar concept is achieved with older characters, the difference being is that they usually rub their Facial Hair or other part of their face instead, probably because nose rubbing is considered more childish.
Use Wiping Nose for wiping blood or a Runny Nose