The unnamed priest in A Farewell to Arms is an important character in that he helps Frederic Henry make sense of his experiences at the front line. Lt. Henry has made an existential choice in his life—to fight with the Italian Army during the First World War. Henry believed that throwing himself into the conflict would give meaning to his life. Yet it has not done so. If anything, his experiences of this terrible war have alerted him to the dark, meaningless void that lies in the very depths of his soul.
The priest is able to supply some of the spiritual wisdom that Lt. Henry so patently lacks. His patience, good sense, and sage advice divest Henry of some of his cynicism and bitterness. Henry's profound disillusionment with the war has had a negative impact on his ability to form meaningful relationships with other people. The priest, despite his avowed celibacy, has a much deeper understanding of love and the enormous sacrifices involved. He reminds us of the universality of love, irrespective of how it manifests itself.
Although some of the other men in Henry's unit poke fun at the priest due to his celibacy, Henry comes to respect him greatly. What he admires most of all about the priest is that he's completely genuine; he's not just going through the motions, dispensing pious platitudes. Despite their evident differences, Henry and the priest are able to connect on an existential level; they've both made a conscious decision to give meaning to their lives. In the case of the priest, this means living according to the example set by Christ, especially in relation to his loving sacrifice on the cross.