But she also spoke in personal terms about her mother Dorothy Rodham, who grew up in an abusive home and was once confined to her room for an entire year for going out on Hallowe'en.
Clinton credited her mother, who died in 2011 at the age of 92, with teaching her tenacity and giving her the strength to try once more to crack what she called "the highest, hardest glass ceiling" in American politics.
The rally on Roosevelt Island, off Manhattan, was delivered nearly seven years to the day after Clinton conceded defeat to Barack Obama in 2008.
While she is the overwhelming favourite to be the Democratic candidate next year, questions linger over whether America may opt for a younger generation rather than the 67-year-old Clinton. She made light of the concern, telling the crowd: "I may not be the youngest candidate in this race but I will be the youngest woman president in the history of the US."
Clinton also assailed the growing pool of Republicans challengers, saying: "We've heard this tune before and we know how it turns out."
The Republican field will grow larger still tomorrow when Jeb Bush, the younger brother of George W. Bush, officially declares his own candidacy - raising the prospect of a rerun of 1992's Bush-Clinton contest.
He has run a de facto race for six months, one that has yet to meet backers' high hopes. His last name guarantees him the highest visibility of any of the many Republicans in the field. But while US media and polls anointed him his party's early frontrunner for 2016, he has not yet lived up to the hype.Telegraph Group Ltd, AFP