[Where does Bill de Blasio stand on the issues? Find out here.]

In precampaign stops in Iowa, South Carolina and New Hampshire, Mr. de Blasio has said that the country is witnessing “the dawning of a new progressive era.” In interviews, he has said that his leadership in New York should be seen as a model for how “you can make profound progressive change and make it quickly.”

He is fond of citing his “pre-K for all” program as a prime example; it was one of Mr. de Blasio’s earliest initiatives, and it remains his largest success. He has also highlighted his role in ending the policing practice of stop-question-and-frisk, which a federal judge ruled discriminated against black and Latino men.

Mr. de Blasio often says that he has a “story to tell” about New York’s accomplishments, but his own narrative is also compelling. He was born Warren Wilhelm Jr. to a German-American father and an Italian-American mother; his father, a veteran who struggled with alcoholism, later killed himself. His relationship with his father was strained, and Mr. de Blasio eventually took his mother’s last name.

Raised in Massachusetts, Mr. de Blasio attended New York University and became a leftist activist who admired Nicaragua’s ruling Sandinista party. He later ran campaigns for Hillary Clinton and Charles B. Rangel, and then ran for office himself, winning elections to become a New York City councilman, public advocate and mayor.

He and Ms. McCray, who has spearheaded ThriveNYC, the city’s mental health initiative, have two children. Their biracial family’s prominence played a large role in his 2013 bid for mayor; a pivotal campaign ad featured his son, Dante, whose giant Afro gained its own following.

Some of Mr. de Blasio’s colleagues have scoffed at the idea of him becoming president and have urged him to abandon his exploration of occupying the White House and instead focus on a bevy of nagging issues in New York City such as crumbling public housing, high levels of homelessness and problem-plagued subways. Mr. de Blasio said that many of the answers for what ails the city actually lie 200 miles beyond its borders in the nation’s capital.

“I am concerned that I think right now our federal government is not helping New York City in a whole host of ways and we’re being hurt all the time by bad policies in Washington,” Mr. de Blasio said at a news conference last month. He cited the lack of a national infrastructure plan and fractured health care policies. “So real changes are needed in our country,” he said. “If they don’t happen, New York City continues to suffer.”