The tree is the central symbol in the novel. It represents the enormous fear in which Gene lived at school, from the summer of 1942 until the spring of 1943. When he was a student at Devon, the tree seemed "tremendous" to Gene, "an irate, steely black steeple beside the river." When Gene does climb the tree, he enters into "a mild state of shock." He jumps from the tree "[w]ith the sensation that I was throwing my life away . . . ."
When Gene returns to Devon after fifteen years, the tree is the main focus of his visit. Going to the river, Gene has trouble even distinguishing it from the other trees. When he does identify it, the tree seems smaller to Gene, "shrunken by age." It seems "weary from age, enfeebled, dry." The tree no longer looms over Gene as some kind of lethal threat. The tree has not changed; Gene has changed. As an adult who has survived Devon and its traumas, he no longer lives in fear.
One possibility for the tree's symbolism is that of falling -- that is, ascending to one's own individual zenith, then failing desperately, descending into a personal abyss.
The reason for this parallel is due to Finny's accident, where he climbed to a great height, then fell after the limb wobbled. After that point in the story, the tree is seen with an air of both superstition and discontent.
The tree could symbolize many things. One of the first things I can think of is that it symbolizes discipline. While some of the older students utilize the tree for military training exercises, Gene, Finny and their friends use it to jump into the river in a friendly sort of adventure game. It represents discipline for the older students in that they are practicing the courage required to jump from a torpedoed naval vessel, but it also represents discipline for the younger boys in that they must muster the courage to leap from a height that is beyond their comfort level. Additionally, they must master their sense of balance and prepare to make a safe leap as well. Gene almost falls once, but Finny catches him and steadies him by the arm. Gene later fails to provide Finny with the same sort of support, allowing him to fall awkwardly and injur himself.
Based on Finny's characterization, the tree can represent a loss of innocence and betrayal. When he and Gene were on the tree limb together, Gene jounces the limb purposefully to make Finny fall, but only a little bit. Finny turns around in surprise and loses balance and falls even though he is the most athletic and coordinated person in the school all because that he trusted Gene that he wouldn't let him fall. Finny has a realization of this as he loses balances, but his mind forces himself not to believe it because his mind wants to protect him from hurt--hurt from losing his best friend because he will lose his ability to participate in sports. At this point, Finny already sensed betrayal, but he forces himself to not believe it because he trusts Gene infinitely. After he shatters his leg from the tree, he slowly develops knowledge of sin which marks his loss of innocence. Through Brinker's kangaroo court at the Assembly Hall in the First Building esp. with Leper as witness, he knows that it was Gene who caused his accident on purpose and he falls down the marble staircase on the way running out to avoid the truth and breaks his leg again. He later dies, but this is all because of his knowledge of sin (loss of innocence by that) and betrayal all starting from the tree and his refusal to believe the truth.
I think that the tree symbolizes maturing over time. At first Gene was really scared of it, but as he grew he became less scared of it. When Finny falls, it makes both boys grow up a lot faster. Then, once Gene returns to it fifteen years later, it is no longer as threatening as it once was.
The tree represents jealousy because that's where Gene makes Finny fall, and it could also represent sacrifice because Gene lost some of his innocence there when he hurt Finny, plus beforehand, people would jump from there to practice for the war.
I hope this helps a little... i tried to be simple, but with a little meaning.