In Kamala Harris’s acceptance speech at the Democratic convention this past summer in Chicago, she sought to cast herself in thoroughly relatable terms. “The middle class is where I come from,” she said, using “middle class” eight more times, as if trying to weave herself into the center of an American electorate that has yet to understand her.

The candidate’s self-description was factually accurate, but what it left out is far more revealing. From interviews with roughly 100 people currently or formerly associated with Ms. Harris, understanding the Democratic nominee for president requires taking her phrase “where I come from” and breaking it into three parts.

First, she is the tenacious eldest child of supremely motivated, risk-taking immigrants: a mother who came from India with the ambition of curing breast cancer, and a Jamaican father who set his sights on shaping his country’s modern economy.

Second, she is the offspring of scientists whose devotion to reason and methodology would guide her in her first career as a law-and-order, linear-minded prosecutor rather than an ideologue. “Fix it,” she would say. Or, “Let’s move on.”

Third, she is the daughter of an Asian woman and a Black man — a human Venn diagram “living in the intersections as a woman of color,” said her friend Mini Timmaraju, the president and chief executive of Reproductive Freedom for All. From Ms. Harris’s childhood in the Berkeley flatlands of California to her current position in the White House, she has lived with the awareness that her gender and racial background have made the world prone to prejudging her.

“It’s not a new thing for her, being disrespected for reasons that have nothing to do with her actual capabilities,” said Jill Louis, an attorney and friend of Ms. Harris since the two were sorority sisters at Howard University. “Does she talk about it? No. Because she’s not a whiner.”