There are many different editions of Lord of the Flies, so the page numbers vary widely. The quoted sentence occurs in chapter 8, about a quarter into the chapter. It is part of the third-person narration.
In this chapter, Jack is challenging Ralph to be the boys’ chief. The earlier mild disagreements between them have escalated into open antagonism. The conflict is fully evident within the meeting that Jack calls, as he tries to get the boys to reject Ralph. When his effort fails, he stalks off in anger.
The other main subject of concern is the boys’ growing conviction that the beast is real. Simon suggests that they climb the mountain to look for it, but the others are reluctant to seek it out. Piggy reminds the group that Ralph has correctly emphasized the importance of making smoke, which a ship or aircraft could see. The problem is that they have let the fire go out.
Piggy’s confidence has been growing because Jack is not present to mock him. He is the one who realizes that the fire need not be made on top of the mountain:
Piggy lifted the conch as though to add power to his next words.
"We got no fire on the mountain. But what's wrong with a fire down here? A fire could be built on them rocks. On the sand, even. We'd make smoke just the same."
The boys realize that he is correct and are relieved they will not need to try and approach the beast, which they cannot even bear to name. Piggy says:
"Of course the smoke won't show so much, not be seen so far away. But we needn't go near, near the--"
The others nodded in perfect comprehension. There would be no need to go near.
"We'll build the fire now."
The greatest ideas are the simplest. Now there was something to be done they worked with passion.