In the first major speech of her second campaign for president, Mrs Clinton portrayed herself as a fierce advocate for those left behind after the recession.
"It's America's basic bargain," Mrs Clinton said. "If you do your part, you ought to be able to get ahead, and when everybody does their part, America gets ahead too.
"That bargain inspired generations of American families, including my own," the former secretary of state and first lady said.
Mrs Clinton launched her campaign in April and has been conducting intimate listening sessions with voters in Iowa and other states with early nominating contests. This was the first large rally of her campaign.
Long one of the most divisive figures in American politics, Mrs Clinton was seeking to use the speech to present herself on her own terms and turn her politicised history into a strength. She lost her 2008 bid for the Democratic presidential nomination to then-senator Barack Obama.
Although the heavy favourite to win the Democratic nomination, she faces a challenge from the left from Vermont Senator Bernie Sanders, who has been attracting enthusiastic crowds in early voting states Iowa and New Hampshire with an anti-Wall Street message highlighting growing income inequality.
Former governors Martin O'Malley of Maryland and Lincoln Chafee of Maryland are also in the race.
She cited Mr Obama, and former presidents Franklin D Roosevelt and Bill Clinton, her husband, and said they embraced the idea that "real and lasting prosperity must be built by all and shared by all".
Her campaign said her "tenacious fighter" message will form the foundation of her 2016 White House race, even as she takes pains to stay silent on politically divisive issues, including two billed by Republicans as key to economic growth - a proposed trade deal with Pacific Rim nations and the Keystone XL oil pipeline.
She gave a nod at the start of her address to the prospect she would be the first woman elected to the White House.
Mrs Clinton told the thousands at the outdoor rally on Roosevelt Island in New York's East River that she was glad to be with them "in a place with absolutely no ceilings".
Eager and excited Democrats began assembling hours before they heard from the candidate.
Those arriving were greeted by campaign manager Robby Mook, who took an all-hands-on-deck approach to the event by hawking merchandise - a role typically assigned to a low-level staffer or volunteer.
After the speech, Mrs Clinton planned to visit early-voting states, with events focused on her relationship with her mother and her father's background as a veteran and small businessman.
"You have to get up off the floor and you keep fighting," Mrs Clinton says in a new video, discussing her failed 1993 attempt to overhaul the nation's health care system during her husband's administration. "Everyday Americans need a champion."