In Lord of the Flies, what does this quote mean: "The rock struck Piggy a glancing blow from chin to knee; the conch exploded into thousand white...

It literally means that Piggy is struck (and killed) by the rock and the conch is destroyed. Symbolically, it means that the talisman which represented order and civilized behavior has also been destroyed. The conch initially established order on the island. Ralph had used it to summon the boys to meetings. He who held the conch was permitted to speak. The conch kept the boys in check. It became a symbol of order and reason. As the novel progresses, more and more boys move to Jack's camp, becoming more like savages. The conch loses its "power" to sustain order. When Piggy and the conch are destroyed, the conch had already lost most of its power, but its destruction makes it complete. 

Piggy is the most intellectual of the boys. He is always trying to reason with them to keep the fire going and to be responsible. With his death, they lose whatever sense of reason and civilized ways they had left. It is tragically fitting that Piggy and the conch are destroyed together. Both the object and the character symbolize reason and order. With their mutual destruction, all of the boys (sans Ralph) have devolved into savagery. Piggy, the voice of reason, and the conch, the symbol of order, die together.