Sexual act. Usually between two males, or a male and a very manly female with anal hair. One partner lays down on their stomach exposing their anus, the other starts from the Gooch or Vagina and sniffs all the way to the Bum Crack, possibly getting some shit stuck in his/her nose.
Joanna the man woman was pleased when John gave her a refresshing Snuffle Bum. Although she acted disgusted.