A fire commonly needs three things: heat, oxygen, and fuel. So:
You put potassium chlorate (the powder) into a container; it'll start to decompose and produce excess oxygen. You apply a blowtorch underneath to provide heat. Then you add fuel - in this case, the glucose in the gummy bear. You then get a fire, fueled by the gummy bear, that fiercely burns off the excess oxygen from the potassium chlorate.
Someone should put on the packaging that gummy bears may explode. This video is proof this can happen. Think of the children.