During a question-and-answer session with reporters at a community center in Compton, Clinton acknowledged the historic nature of her candidacy and likely nomination after being asked if she feels the "weight of what this means for people."
"I do, I do," Clinton said. "I've seen it for more than a year. My supporters are passionate. They are committed. They have voted for me in great numbers across our country for many reasons, but among those reasons is their belief that having a woman president will make a great statement, a historic statement about what kind of country we are, what we stand for."
Clinton, who earlier declined to directly reflect on the history, said the weight is "really emotional."
"I am someone who has been very touched and really encouraged by this extraordinary conviction that people have. It's predominantly women and girls but not exclusively. Men bring their daughters to meet me and tell me that they are supporting me because of their daughters."
Clinton added, "And do I think it will make a very big difference for a father or a mother to be able to look at their daughter, just like he can look at their son and say you can be anything that you want to be in this country including president of the United States."
The former secretary of state has largely declined to discuss the historic nature of her candidacy. It wasn't until recently, however, that Clinton began addressing her status as the potential first woman nominee for a major political party.
"I know we have never done this before," Clinton said on Saturday in Fresno. "We've never had a woman president. That is why I want you to understand, that I have spent eight years in the Senate on the Armed Services committee, four years as secretary of state."
Clinton ran away from the historic nature of her candidacy during her failed 2008 presidential campaign, instead trying to focus on her preparedness in an effort to show her toughness.
But when Clinton launched her campaign in 2015, she did so in a softer light, as a grandmother who wants to talk about "kitchen table" issues like health care, education and social services.
Clinton, who is currently 26 delegates shy of surpassing the number of delegates needed to clinch the Democratic nomination, is expected to do so on Tuesday, when states like New Jersey and California hold their primaries.
Those votes will come in eight years to the day after Clinton ended her 2008 campaign and urged her supporters to "help elect Barack Obama, the next president of the United States."
"Although we weren't able to shatter that highest, hardest glass ceiling this time, thanks to you, it's got about 18 million cracks in it, and the light is shining through like never before, filling us all with the hope and the sure knowledge that the path will be a little easier next time," Clinton said at the time.
On Monday, Clinton was asked if Sanders should endorse her like she did Obama.
"We'll wait and find out," the former secretary of state said. "Actually tomorrow is eight years to the day after I withdrew and endorsed then-Senator Obama. I believed it was the right thing to do no matter what differences we had in our long campaign."