The phrase "open nostrils" means that the holes in your nose through which you breathe are clear and not blocked.
Sentences with «open nostrils»
The large eyes are dark and round; the nose should be black with open nostrils; the body is compact, with sloping shoulder blades and fairly deep chest. (puppiesdogs.org)
Nose: The nose is large with wide open nostrils. (abra1st.com)