Assef is simply a bully. This is shown through both direct and indirect characterization. Assef carries around his legendary set of brass knuckles, which he uses to pummel anyone weaker or deemed to be less worth than him. He also has his two cronies that follow along and "co-sign" on all of his malicious deeds.
Indirectly we hear tales about the brutalities he inflicts on other children, including one that is disabled. We also find out about the sexual abuse of Hassan's son indirectly at the end of the novel.
Directly we see the rape of Hasssan through the eyes of Amir and his cruel, murderous, vengenful side when he and Amir are fighting at the end of the novel.
We also directly see that Assef's outer appearance does not truly show his inner character. At Amir's birthday party, it is clear that Baba admires Assef and wishes that Amir were more athletic, outgoing and attractive like Assef, and like Baba in his youth.
Assef is also shown to love Hitler and to believe in ethnic cleansing, which is supposedly one of the motivating factors for his sadistic behavior.