The pomegranate tree is a symbol of friendship and of Hassan's martyrdom in The Kite Runner. The friendship between the youthful Amir and Hassan flourishes and then dies under the boughs of the pomegranate tree where the two once played. As if to emphasize this tree as a symbol of their bond, Hosseini has Amir carve his and Hassan's names on its trunk. Amir at this point naively treats the two of them as equals, identifying them both as "sultans," although it will be class inequality that rips them apart.
Significantly, the pomegranate is one of the four holy fruits of Islam, the religion of both boys, a status that the fruit derives from the Jewish tradition in which Islam is rooted as a religion of the Book. Jewish priests, as described in the Torah, had pomegranates embroidered on their priestly robes as a symbol of the abundance and fertility God gave to the Jewish people.
From the start, the red of the pomegranate is likened to blood, and later in the novel, the juice of the pomegranate, staining Hassan, becomes a symbol of his martyrdom: he sacrifices himself for Amir. Amir sits under the tree and pelts his friend with the pomegranate fruits, hoping Hassan will alleviate his guilt over the rape by striking back. Instead, Hassan takes the abuse without retaliation:
Hassan was smeared in red like he'd been shot by a firing squad.
Hassan adds a Christlike note to the symbolism when he crushes a pomegranate on his forehead. It drips "down his face like blood" just as the crown of thorns caused blood to drip on Christ's face.
As time goes on, "droughts" impact the tree so that it no longer bears fruit, a symbol of the way the friendship between Hassan and Amir has dried up.