Prim, Katniss's little sister, seems like a bright light in a dark world:
I look at my little sister and think how she has inherited the best qualities our family has to offer: my mother's healing hands, my father's level head, and my fight. There's something else there as well, something entirely her own. An ability to look into the confusing mess of life and see things for what they are. (13.31)
If Katniss has done anything good in her life, it's taking her sister's place in the arena so Prim could have a fair shot at growing up and sharing that "something entirely her own" with the world. Katniss sees Prim as the "best" part of her family, a combination of the best characteristics they all had to share. She's becoming an adult, and a good one. The "little girl" Katniss went into the arena to protect has already vanished:
She's really gone, then. The little girl with the back of her shirt sticking out like a duck tail, the one who needed help reaching the dishes, and who begged to see the frosted cakes in the bakery window. Time and tragedy have forced her to grow too quickly, at least for my taste, into a young woman who stitches bleeding wounds and knows our mother can hear only so much. (3.8)
In a way, Katniss has already lost her little sister. But for much of Mockingjay, it seems like in her place Katniss has gained a friend and ally – someone who can help her make sense of the crazed world around her and trust in some kind of hope for the future:
Prim a doctor. She couldn't even dream of it in 12. Something small and quiet, like a match being struck, lights up the gloom inside me. This is the sort of future a rebellion could bring." (10.72)
When Prim dies, it seems like Katniss's hope for the future might be dying too, since Prim is the one who made Katniss find that hope in the first place. Prim dies when she's only thirteen. She never got a chance to grow up and be a doctor. She was stuck between being a child and an adult, and had just started to find her wings.
Prim's death reveals to Katniss an important truth. Just as Prim being selected for the Hunger Games showed Katniss the Capitol cruelty, Prim's death reveals to Katniss the cruelty of President Coin, who was responsible for the girl's slaughter.