To most who saw the quotation being circulated this week as a meme, it was just something funny that Kamala Harris said in a speech in 2023: “You think you just fell out of a coconut tree?”

But for many Indians and Indian Americans, the line, which Ms. Harris attributed to her mother, is layered with extra meaning. Tamil Nadu, the South Indian state where her mother’s family is from, is one of India’s largest growers of coconut palms. It’s also the kind of thing an Indian parent might say.

Ms. Harris, the vice president and Democratic candidate for president, neither advertises nor shies away from her Indian heritage. She slips in references to it. She also deploys it strategically.

Last year, Ms. Harris spoke of her deep personal connection to India at a luncheon in Washington for Narendra Modi, the Indian prime minister, whom the United States has been courting. Her introduction to the concepts of equality, freedom and democracy came from her Indian grandfather, Ms. Harris said, with whom she went on long walks during her visits to Chennai.

“It is these lessons I learned at a very young age that first inspired my interest in public service,” she said.