Epigraphs are like little appetizers to the great entrée of a story. They illuminate important aspects of the story, and they get us headed in the right direction.
"This book is to be neither an accusation nor a confession. It will try simply to tell of a generation of men who, even though they may have escaped its shells, were destroyed by the war."
In a gloomy and slightly strict tone, this epigraph sets out the matter-of-fact style that is an essential aspect to this story. Our narrator speaks in this same gloomy and slightly strict manner. This epigraph sounds almost journalistic and neutral, leaving us to assign love or blame as we read the novel. In this way, the epigraph sets us up for the emotional temperature of the oncoming novel.
More intimately, this is the epigraph of Paul Bäumer, the main character. It is his story and it is his life's destruction (emotional and physical) that will show us how war destroys humanity. His story itself is charitable, life-affirming, and hopeful. The fact that he's telling his story demonstrates that he had hope somewhere inside of him that it would mean something to others, that it might motivate others to help change the dynamics of war.
At the end of the novel, we are reminded of the epigraph, for Paul appears relieved to be done with life. Because of Paul's need to kill his soft, kind, personal inner self in order to survive, Paul had died emotionally long before his body was physically dead. So throughout the story, though Paul's body had escaped physical damage, his inner self had been destroyed by the war. We are left to assume that other men, those who survived the entire war, were also destroyed by it.