They met more than two decades ago, when Ms. Jarrett — a lawyer, like both Obamas — offered Mrs. Obama a job in the Chicago mayor’s office. Ms. Jarrett was a single mother who had come up the ranks of city government, the daughter of a prominent African-American family. Her grandfather, Robert Taylor, built much of Chicago’s public housing, her father was a pioneering doctor, and her mother had a Chicago street named after her for her work in early childhood education. Mr. Obama was a rootless but ambitious Harvard law graduate, looking to make a political name. At their first dinner, they talked about a “philosophy of empowerment” for the downtrodden. “That’s where we clicked,” she later told Ms. Sher, and from then on she was determined to introduce Mr. Obama, almost five years her junior, to the activists and donors he needed to move first to the legislature and then to the United States Senate.