Piggy's glasses symbolize a connection to civilization and to scientific reasoning that generally erodes through the conflict in the novel.
In the first chapter, Ralph asks Piggy about his father, and Piggy takes off his glasses before answering:
“My dad’s dead,” he said quickly, “and my mum—”
He took off his glasses and looked vainly for something with which to clean them.
In this moment of emotional discord, Piggy removes his glasses and looks around vainly without them. This is important as it demonstrates Piggy's difficulty in reasoning his way through this emotionally-laden response. When the glasses come off, Piggy's ability to reason also falters.
When the group comes together later in that same chapter to discuss their options for survival, Piggy is seen putting on his classes before clearly assessing their dire situation:
Piggy put on his glasses.
“Nobody knows where we are,” said Piggy. He was paler than before and breathless. “Perhaps they knew where we was going to; and perhaps not. But they don’t know where we are ’cos we never got there.” He gaped at them for a moment, then swayed and sat down.
Piggy's sense of rationality is clear here. He understands their grim situation and applies a scientific understanding of planes, flight schedules, communication, and probability to their likelihood of being rescued. But before he can utter those, words, Piggy must first put on his glasses, which presents him as a symbolically trustworthy form of knowledge on the subject.
The boys determine that they should use Piggy's glasses as a fire-starter, indicating the power of scientific reasoning to bring survival to this world of savage disorder:
“Here–let me go!” His voice rose to a shriek of terror as Jack snatched the glasses off his face. “Mind out! Give ’em back! I can hardly see!"
It is important to note that the glasses are stolen from Piggy, demonstrating the lack of respect that Jack holds for reasoning and knowledge. Instead, Jack acts in emotional passions, a contrast to Piggy's solid sense of steady reasoning.
Once Jack's tribe steals what remains of Piggy's glasses, Piggy is left virtually powerless against their efforts to annihilate what remains of Ralph's group. He becomes frightened, and his speech echoes a lack of reasoning. When Ralph and Piggy make one final attempt to reclaim Piggy's glasses and a sense of order, Piggy is killed by Jack's tribe. This demonstrates Jack's complete disconnect from civilization and societal order.