This allowed the contrast in their personalities to be even more prominent and their characteristics became even more obvious. Some good examples from Shakespearean plays would Brutus and Cassius, Iago and Othello and Macbeth and his wife. If we look closely Iago and Othello's relationship was such that whenever they came together in one scene, we could immediately spot the differences in their personalities and their qualities. While Iago was cunning, scheming and manipulative, Othello was noble, simple and trusting. Exactly this is how Amir and Hassan's relationship worked in Kite Runner too. While Amir wanted to get his way each time and was not even very loyal, Hassan could give his life for Amir. Amir escaped from a horrifying incident in which Hassan was directly involved while Hassan would have risked his life to save Amir. This was a contrast in their personalities. And it was because of Amir that Hassan was driven...

Amir accused Hassan of stealing his watch which he himself had placed his Hassan's room. He simply wanted to drive Hassan out because he reminded Amir of his own cowardice. Hassan would have never done something like that to Amir. The contrast in their qualities and personalities became very prominent when each time these two were together. Thus Hassan was acting as a foil to Amir and this is exactly how foil arrangement works in literature.
Reference

William Henry Hudson. An introduction to the study of Literature. 2007

Alfred Hennequin. The Art of Playwriting. 1890