Like beauty, symbolism is in the eye of the beholder, or in this case, the reader. In one way, the tree serves a function in the story. Climbing the great pine allows Sylvia to spot the white heron from high above the forest. She climbs the tree to find the heron's nest so that she can tell the hunter, thus pleasing him and earning the money her grandmother needs.
However, Sylvia's climb up the tree is quite difficult and dangerous, requiring much bravery and strength. Once she reaches the top, she experiences the natural beauty of the world in a way that she never would have known had she not made the climb. She leaves her own world and lives for a little while in the heron's world. What she sees and feels at the top of the pine tree changes Sylvia in a profound way, and she can no longer give the heron up to destruction at the hands of the hunter.
The fact that the story's climax concerns Sylvia climbing the pine tree suggests that it has a meaning greater than its literal fact. Sylvia's climb might be interpreted as her growing up, finding her own identity and values. This isn't easy, but the rewards are great. After climbing the great pine, Sylvia has realized something important about herself and how she will live her life.