In order to know the significance of the conch shell shattering, it helps to think about what the conch shell was symbolic of while it was still in one piece. Early on in the story, the boys attempt to set up a democracy of sorts. There is a head chief, but the conch is equivalent to a microphone. Whoever is holding the conch gets to speak, and everybody is supposed to listen. The conch gives everybody an equal voice.
"That's what this thing is called. I'll give the conch to the next person to speak. He can hold it when he's speaking."
Readers might then say that the conch is symbolic of law, order, civility, democratic rule, and/or civilization. When the conch is destroyed, all that it stood for is also destroyed. The idea that all ideas could be voiced with mutual respect is gone, and all that remains is Jack's reign of terror through the concept of might makes right.
The conch is also symbolic of Ralph's power. He is the boy that first blows the conch, and that helps to establish him as the leader.
But there was a stillness about Ralph as he sat that marked him out: there was his size, and attractive appearance; and most obscurely, yet most powerfully, there was the conch. The being that had blown that, had sat waiting for them on the platform with the delicate thing balanced on his knees, was set apart.
When the conch is destroyed, it is also a great symbolic image that Ralph's time as leader is completely finished.