The male s nose is so long, it may hang down right over the mouth, and he has to push it up and out of the way when he eats. The nose swells and turns red when the monkey is enraged or excited. But it doesn't inflate. He does this when he senses danger and perhaps just to attract the ladies.
Females have smaller noses, and juveniles have small upturned noses.
Another is that his large nose helps the male to cool off by radiating excess body heat. But the most compelling suggestion is that females prefer males with big noses, thus selecting for offspring with big noses. Tail about the same length as the body. One young born. Gestation about 166 days.