Father may be frail and old at first glance, but he is the family patriarch, and a source of serious wisdom and experience, especially for Parvana. A former history teacher, pretty much every time Father opens his mouth, a gem comes out, like:
[…] never rely on the railing. (1.58)
Father was crippled by a bomb, and needs help getting to and from market each day (a job that Parvana happily does)—and yet, when they come home each night, he doesn't use the railing on the stairs in their bombed-out apartment building. But Father isn't just being literal when he tells Parvana to "never rely on the railing"—it's a metaphor, too, and he is also telling his daughter to rely on herself first and foremost, which, in a country riddled by war and violence, is pretty sound advice. And he says it all in a few simple words.
Father's wisdom doesn't always come out in one breath, though, and with few belongings left to entertain themselves with, the family gathers around him after dinner each night as he entertains his children by "telling stories from history" (2.50). He might not be able to officially teach anymore (thanks to the Taliban), but school is definitely in session for his kids each evening.
His most noteworthy story is about the legend of Malali, a little girl who inspires the Afghan soldiers to fight against the British invaders. Father knows how important it is for his daughters to be strong, educated, and independent—particularly since the Taliban tries so hard to make women the opposite—so he tells them:
You are all brave women. You are inheritors of the courage of Malali. (2.61)
As his daughters grow up in a society that insists on their invisibility (they literally cannot leave the house without a man, and then are expected to be completely covered), Father gives them a different lineage to place themselves in—the lineage of Malali—and by doing so, reminds them about how powerful and brave women can be. The story of Malali is particularly meaningful for Parvana, and she remembers her Father's story several times while he is imprisoned and uses it as a source of strength (check out her analysis elsewhere in this section for more on this).
Speaking of being imprisoned, we don't actually see Father for much of the book, since Taliban soldiers raid the family apartment early on in the story, tearing through it and taking Father off to prison without ever offering a reason. And then—after Mother and Nooria and the little kids have left—Father is just as mysteriously released and comes home. When he does, though, he is "barely recognizable" (15.1), and because of this we get a sense of how cruel life inside Taliban jails is.
It is important to note that Father is the only positive male figure in the book. Since the Taliban is entirely male, he serves as a reminder that though life in Afghanistan at this time is intensely violent and oppressive to women, it doesn't have to be this way—it is entirely possible for men to be kind, gentle, and thoughtful people who treat women with the respect they deserve. And yet because Father is the only man like this that we ever see, we also get the sense that he is exceptional and that, as such, better times remain far off in the distance.