That line appears in the final paragraph of chapter one. Jack has just failed to kill a wild pig that he came across in the forest. He failed because he hesitated. He hesitated because he had never killed anything before, and the amount of blood probably had him worried.
They knew very well why he hadn’t: because of the enormity of the knife descending and cutting into living flesh; because of the unbearable blood.
Jack scolds himself about his failure because it makes him look weak in front of Ralph and Simon. The text says that Jack then took his knife out of its sheath and drove the blade into a tree trunk. He then vowed not to hesitate to kill at the next opportunity.
He snatched his knife out of the sheath and slammed it into a tree trunk. Next time there would be no mercy.
The quote is important because it foreshadows the murderous person that Jack is soon to become. This moment is just about the last time that readers see Jack with some sort of moral compass. From here, he becomes a much colder, harder, and efficient killer.
He says this after he refrains from killing the pig that they see when they are exploring. He shows that he has savage tendencies. He's aggressive with his choir, as he doesn't seem to care when Simon faints. He even slams his knife into a tree, which shows his short temper. When he holds back from going after the pig, he shows that he has some civility. However, his scary comment of "Next time there would be no mercy" shows that he will not hold back next time.
In a later chapter when he first gets blood on his hands, he grimaces a bit and wipes his hands off on his pants. It doesn't take long for him to have no reaction to the killings as time goes on. So this quote shows where Jack began, and it foreshadows the savage beast he becomes later on.