Gale designed a bomb that killed Prim while she went to heal another kid hit by a bomb. Gale went to district 2 and got a job there. Katniss killed President Coin and caught on fire by the bomb that killed Prim. Finnick died too.
Wait, Gale... killed Prim...?
It was his bomb that killed her but he never dropped them. Some other rebels took control of the capital hover plane and dropped the little silver parachutes into a crowd of kids. When the kids went to grab them, some of the packages exploded. The rebel medical team, which included Prim, went to go help the surviving kids when the rest of the packages exploded, killing her.
And Coin dropped the bombs, if I recall... But why?
I'm not sure. I read it around my mom's boyfriend's kids and their so loud I must have skipped it by mistake. :/
To turn the Capitol citizen's against Snow. The children being hit by the bombs in the first place where Capitol children that Snow had ordered into a protected area. The Capitol turns on it's own children, then the rebels come in to save them and get killed in the process. This turns the citizens sympathies to the rebels, making taking over the government easier.
Sending Prim in also acts as a duel purpose against Katniss. It punishes her for going off on her own against Coin's wishes and manipulates her emotions and thoughts so she is easier for Coin to control. And it was working to, until Katniss found out about it.