Vladimir's father (who is basically only ever referred to as "my father") serves as the political context of the book, in the form of a brave, hyper-principled, and outspoken liberal thinker, writer, and jurist. (FYI: a "jurist" is someone who studies and writes about the law/a lawyer who doesn't participate in trials, but could be a judge.) Where his son is glamoured by the beauty of childhood, Vlad's dad is out there on the front lines.
Let's talk for a second about his political views in relation to the book. The elder Nabokov was raised in a Tsarist-supporting family, people who were part of the royal court and ministers to the governing body. The family enjoyed wealth, power, and influence, and Vladimir's grandma was none too pleased when his father decided against following in the family footsteps.
Instead, he becomes a liberal activist, who speaks out against police involvement in anti-Jew pogroms (riots). Once Tsarist rule ends, the two major parties of Russia are the Communists (AKA Bolsheviks) and the Liberals. Most of the liberals are rich, like Vladimir's father, and believe in civil liberties, universal voting rights, labor reforms, and minority rights. Meanwhile, the Bolsheviks are led by Vladimir Lenin. They believe in a single-party state, governed by a small council who would make most of the decisions, while eliminating social classes, and with everybody contributing to either the labor or the political advancement of the country. Sound a bit dystopian? You're not alone.
As the Bolsheviks gain power, Vladimir's father can see the writing on the wall, and trucks his family out of harm's way. But he remains invested, and continues to write for liberal newspapers abroad. He can't stop, and his clear, forward-moving activism is a foil to dreamy Vladimir's time in the maze of childhood and adolescence. Eventually, as we know, it gets him killed. Though Nabokov doesn't discuss directly the impact it had on him, it can be seen elsewhere, as he brings up the fact of his father's death, over and over, as if he wants the fact to change.