The apple tree is symbolic in many ways. First, it was planted in the memory of Larry, the eldest the the Keller children whose plane was shot down in the World War II. Apple trees are universal symbols for the sin and the fall of mankind from the garden of Eden. Trees are also personified as men in the Bible. In Song of Songs, the apple tree is also associated with mothers and sons and also, sons and lovers.
In Song of Sons 8:5 we read:
"Who is this that cometh up from the wilderness, Leaning upon her beloved? Under the apple-tree I awakened thee: There thy mother was in travail with thee, There was she in travail that brought thee forth."
In Son of Songs 2:3, As the apple-tree among the trees of the wood, So is my beloved among the sons. I sat down under his shadow with great delight, And his fruit was sweet to my taste. (ASV BBE DBY JPS WBS)
The the apple tree foreshadows some kind of break in the relationship between Larry's mother, who still believes he is alive, and also the blossoming relationship between Chris and Ann. The tree can also be seen as representing the Keller household which hides the sin of the father That sin and its consequences are about to break the family apart. The significance of the letter is that it proves that Larry was suicidal over his father's crime and that he was planning to let himself be shot down. The letter shows that Larry was like the apple tree, torn apart by the story over his father's actions.