What is the significance of the summer session?

I think that the significance of the summer session is best viewed symbolically in contrast to the winter session. The summer session is a much slower pace of things for the boys on the Devon campus. They are freer to be kids because there is less oversight on their behavior and fewer time commitments in terms of their schedule. They get to play during the summer session, and I think the summer session can be used to represent things like innocence, peace, and youth. The war is happening, but it is such a distant concern that characters are even able to make comments about how there isn't actually a war. The winter session stands out in stark contrast. It could represent rules and authority. With school in full session and friends going off to the war and returning with a full mental breakdown, the winter session very quickly turns the boys from kids to adults.
The summer session is also important in terms of character building. Through the summer session, Knowles is able to show readers exactly how carefree, gifted, and altruistic Finny really is. That characterization is key to understanding how warped Gene is internally. Gene is our narrator, yet we have a really hard time fully liking him because of his growing jealousy and dislike of Finny. The summer session is critical to readers because it sets up that friendship base that falls apart so completely by the story's conclusion.

Written in the retrospective point of view with Gene Forrester narrating the events of his final year at Devon School, the novel is structured primarily as a flashback that develops chronologically from the summer of 1942 through the spring of 1943. Throughout the novel, Devon and the atmosphere at the school are often described in relation to the changing seasons. The motif enhances the setting and establishes the passage of time, but more significantly, it contributes to thematic development. The changing seasons parallel Gene and Finny’s emotional states and the encroachment of World War II into their lives and the lives of their classmates. In drawing these literary parallels, John Knowles unifies the novel and enhances the drama and the poignancy of its primary theme: the destruction of innocence. In the novel’s chronology of seasons, summer is the season of innocence, the brief, transitory time at Devon that precedes the unrelenting loss of illusion.
In the summer of 1942, World War II is raging in Europe and the Pacific, but under the “open New Hampshire sky,” Devon is a refuge of peace and natural beauty. Gene describes summer at Devon in vivid detail, recalling the “healthy green turf” of the playing fields “brushed with dew” and the “faint green haze hanging above the grass, shot through with the twilight sun.” He remembers hearing “the cricket noises and the bird cries of dusk.” The woods beyond the playing fields and Devon’s two rivers underscore the presence of nature at the school and serve to emphasize Devon’s tranquil separation from the war and from the world at large.
The atmosphere at Devon during the Summer Session is careless and undisciplined; with most of the students and the regular faculty away, the pace is slower, and the rules are rarely enforced. Summer is a time for swimming in the pristine Devon River and playing games. Leper collects snails, and Gene and Finny make an illicit overnight bicycle trip to the beach. Gene recalls, “We spent that summer in complete selfishness, I’m happy to say. The people in the world who could be selfish in the summer of 1942 were a small band, and I’m glad we took advantage of it.” Central Europe is being bombed, but the devastation of war seems unreal to the boys at Devon. “Our place here was too fair for us to accept something like that,” Gene remembers. Throughout the summer, the reality of war is pushed aside, and the illusion of peace prevails.
Although Gene and Finny generally ignore World War II as the Summer Session continues, they think of the war from time to time as they go about their daily activities. They play “blitzball,” a game Finny invents that is named for the German “blitzkrieg,” and Finny acknowledges the bombing of Central Europe in a conversation with Mr. Patch-Withers. Finny’s discussion of the war, however, is offered only as a nonsensical explanation for his having worn a pink shirt to the Headmaster’s Tea. The war does not become real to Gene and Finny until the following spring when they realize how completely it has destroyed Leper Lepellier’s mind and spirit.
During the summer of 1942, Gene and Finny could not have imagined Leper’s ultimate destruction, nor could they have imagined Gene’s betrayal and Finny’s death. The innocence of youth was yet to be shattered by the reality of war and by the knowledge of the human impulse to strike out blindly in ignorance, fear, and hatred. As the season draws to a close, Finny is irreparably damaged, and Gene has begun his painful psychological struggle with shame, guilt, fear, and remorse. Summer and all that it suggests about youth and innocence ends “in the last long rays of daylight at the tree, when Phineas fell.” Remembering Gene, Finny, and their “gypsy band” as they had been in Devon's beautiful summer of 1942 makes their loss of innocence tragic.