In Saigon, Hà has managed to grow her own papaya tree from seed. As the tree grows taller and taller it becomes the little girl's pride and joy. She loves nothing more than watching it grow, in the hope that one day it will bear delicious fruit.
But the papaya tree is more than just a plant; it has deep symbolic significance for Hà. Like her, it is firmly rooted in Vietnamese soil. As such, it represents the country of her birth, the country of which she's proud, the country she will always call home. Just as she wants to see the papaya tree grow and prosper, she also wants the same for her country.
Even when Hà's in the United States, thousands of miles away from her native land, thoughts of the papaya tree are never far from her mind. Hà longs for the tree and its delicious fruit, which she simply cannot find in America. Once again, there is deep symbolism at work here: the fruit of the papaya tree symbolizes herself. Her inability to find delicious papaya fruit in the United States therefore represents her sense that she can't find herself in America, that she doesn't truly belong in her new home. Like the papaya tree she's rooted in Vietnamese soil, and can only really thrive there.