Analysis by Chris Cillizza, CNN Editor-at-large

(CNN) -- It's been a bit of a rough start for Massachusetts Sen. Elizabeth Warren's 2020 presidential campaign.

She's been hounded by her botched handling of claims of Native American heritage and has watched as fellow senators like Bernie Sanders and Kamala Harris have zoomed past her in the early jockeying for the chance to take on President Donald Trump next November.

Which makes what happened Monday night in Jackson, Mississippi, very important for Warren and her supporters. At a CNN-sponsored town hall, Warren delivered a very strong performance in which her policy chops, which we knew about, were bolstered by the powerful -- and emotional -- re-telling of her childhood struggles.

One moment in particular stood out. Here's the exchange between Warren and CNN's Jake Tapper:

TAPPER: You talk about how your family stood at the brink of financial disaster through a good part of your childhood. How has that shaped your life in the Senate?

WARREN: I'll tell you about that. I have three older brothers. They all went off and joined the military. That was their ticket to America's middle class. I was the late-in-life baby. My mother used to call me the "surprise" and about the time I was in middle school, my daddy had a heart attack and it was serious. Thought he was going to die. The church neighbors brought covered dishes. It was a scary time. He survived but he couldn't go back to work. We lost our family station wagon and at night I would hear my parents talk and that's where I learned words like mortgage and foreclosure and I remember the day that I walked into my parents' bedroom and laying out on the bed is the dress. And some people here will know the dress. It's the one that only comes out for weddings, funerals and graduations and my mother is in her slip and she is stocking feet and she's pacing back and forth and she's crying. She is saying "we will not lose this house. We will not lose this house." She was 50 years old. She had never worked outside the home. She was truly terrified. And I watched her while she finally just pulled it together, put that dress on, put on her high heels and blew her nose and walked to the Sears and got a minimum wage job, and that minimum wage job saved our house, but more importantly, it saved our family.

To get the full effect of the answer, you need to watch it. Warren is visibly emotional, her eyes welling up with tears as she recounts the courage of her mother. Watch this:

(The Warren campaign, sensing their candidate had just had a moment, tweeted out the video of her answer.)

Why did this moment matter? Because presidential campaigns are about moments, about glimpses into who a candidate really is and what motivates them to run for the highest office in the country.

For most voters, Warren was just a jumble of policy proposals before Monday night. She is a self-admitted policy wonk who has put her meaty policy prescriptions front and center in the campaign. But voters don't choose a candidate based solely on policy papers. If they did, every president would be a former think-tanker. Who the candidate is, really, plays an absolutely critical role in the presidential decision. At root, people usually vote for president based on a belief that the person they are choosing "gets" them in some fundamental way.

Which brings me back to Warren's emotional recounting of her family's economic struggles and her mother's bravery in the face of possible financial ruin. It wasn't the first time she's told that story. As MJ Lee, who covers Warren for CNN, noted, that retelling of her childhood is a staple of Warren's stump speech. But most people haven't seen a Warren stump speech. They have likely read or seen coverage of her struggles to clear up whether she is of Native American descent (or not). Maybe they know she is a senator from Massachusetts who previously worked in the Obama administration. But that's about it.

Warren's powerful delivery of her childhood struggles Monday was on national TV and in primetime. Lots and lots of people either saw it live, watched a snippet of it on social media or read about it on a website just like this one. That matters. To win a presidential nomination, you have to be able to perform when the bright lights come on and everyone is watching.

Warren did that on Monday night. Which should serve as a shot of momentum for a campaign that needs it.