Through the character of Jack, a reader is able to witness the complete abandonment of morality. Or you could say that Jack provides the reader with evidence as to how evil tendencies arise with no society to keep them in check. However, in describing Jack, it's clear by the end of the story that he is no longer a sweet choir boy. He's a sadistic, narcissistic, murdering dictator of a leader.
He raised his arm in the air. There came a pause, a hiatus, the pig continued to scream and the creepers to jerk, and the blade continued to flash at the end of a bony arm. The pause was only long enough for them to understand what an enormity the downward stroke would be.
Chapter one's pig sequence is important to the story and in terms of Jack's character development, because it does two things. First, it shows that Jack is capable of restraint. He understands that by bringing down the knife he will be taking a life. Jack isn't ready to be that guy yet. He hasn't fallen far enough away from societal norms and rules to make killing a reflex action . . . yet.
The scene also serves as a way to foreshadow what Jack will become by the end of the book. It's fairly obvious that Jack will get another chance to kill a pig, but just in case a reader might miss it, Golding drops a huge hint moments later.
Next time there would be no mercy. He looked round fiercely, daring them to contradict.
The piglet sequence shows what Jack is, and it shows what he will become.