You know those scenes in films that just scream "bolt of lightning"?
During the liquidation of the ghetto, Schindler spots a little girl running through the streets in a red coat. We know that because it's one of the only instances of color used in the whole film, with the red coat standing out in stark contrast to the rest of the black and white scene.
What's so important about that coat? What's Spielberg saying with it?
First, it's the moment when Oskar truly gets it. He sees the chaos of the liquidation and gets punched in the gut with the horror of it all. Spielberg means for us to see this as a moral turning point for Schindler. The color drives the point home and focuses Oskar on the humanity of the people who are being treated like animals.
Second, it's a powerful way to individualize the horror. It's easy to become numb to the murder of millions. There's a saying, sometimes attributed to Joseph Stalin, that "One death is a tragedy; a million deaths is a statistic." Even Mother Teresa once famously said, "If I look at the mass I will never act. If I look at the one, I will." (Source)
That's why it's easy to do nothing about mass tragedies until our attention can be focused on one person's story: The Syrian refugee boy washed up dead on the beach; the starving child; the famous photo of the girl on fire from napalm during the Vietnam war. These individual stories move people to compassion and, we hope, action.
In the scene of the girl in the red coat, we focus on one life. Multiply that girl by two, those girls by four, those girls by sixteen, and you can see where this is going. Spielberg wants to show us one drop in the ocean of monstrous loss, to understand exactly the human dimension of the six million Jews killed.
And just so we're absolutely clear about the "killed" part, Spielberg returns to the red coat (and the girl who owns it) a second time… when her body's in a wheelbarrow headed to be burned with thousands of other corpses. It's a shocking moment.