In Jefferson's trial, his defense attorney tries a pretty offensive bit of reverse psychology on the jury. He tries to tell them that they're right about Jefferson not even being a man, and for that reason it's not even worth killing him:
"Gentlemen of the jury, be merciful. For God's sake, be merciful. He is innocent of all charges brought against him.
But let us say he was not. Let us for a moment say he was not. What justice would there be to take this life? Justice, gentlemen? Why, I would just as soon put a hog in the electric chair as this." (1.15-16)
What a total racist scumbag. If that attorney had lived in the age of smart phones and YouTube, he never would have heard the end of it. But even though his statement wasn't broadcast into the interwebs, it still had profound effects on the people that heard it.
Miss Emma takes it seriously and makes it her life's mission to make sure Jefferson goes to the electric chair as a man, and not a hog. She enlists everyone around her to help prove that attorney wrong:
"Called him a hog."
[. . .]
"I know he was just trying to get him off. But they didn't pay that no mind. Still gave him death."
She turned her head slowly and looked directly at me. Her large, dark face showed all the pain she had gone through this day, this past weekend. No. The pain I saw in that face came from many years past.
"I don't want them to kill no hog," she said. "I want a man to go to that chair, on his own two feet." (2.44-48)
What Miss Emma means by this is that she wants Jefferson to know that he is a man. She isn't as worried about whether the judge or jury knows; she wants her boy to know.
"I want the teacher make him know he's not a hog, he's a man. I want him to know that 'fore he go to that chair [. . .]" (3.36)
For Emma, the teacher is the obvious choice for, well, teaching Jefferson that he is a human being, not a hog.
The image is almost always used in conjunction with Jefferson himself. However, we learn why the hog is such a handy image for the people in and around Bayonne. The town's "major industries were a cement plant, a sawmill, and a slaughterhouse, mostly for hogs" (4.10). This little bit of information, hidden in the middle of the description of the town, reminds us of just how inconsequential and ordinary Jefferson's death will be to the majority of the people in Bayonne.
Several people refer to Jefferson as a hog throughout the novel, but the most disturbing instance is when he does it himself. He asks for corn to eat (because pigs love corn) and says that he's getting fattened up for Christmas. Then he calls himself an "old hog" and performs for Grant:
"I'm go'n show you how a old hog eat," he said.
He knelt down on the floor and put his head inside the bag and started eating, without using his hands. He even sounded like a hog. (11.58-59)
This dehumanizing action shows just how much Jefferson has taken the public defender's words to heart, and how little he values himself because he knows that society doesn't value him, either.
The symbol of the hog in A Lesson Before Dying has its roots in history. During slavery black people were treated as possessions, in the same way that livestock were regarded as possessions. The Three Fifths Compromise dictated that, for tax purposes, a black person was worth three-fifths of a white person. What Jefferson and his community is dealing with isn't one hack attorney's poor choice of words; it's a history of subjugation and black people being considered as a lower species than white people.
Basically, the hog symbolizes all the freaking horrible, awful, messed-up thinking that went into slavery in the first place… and then persisted in the form of Jim Crow laws and racism.
But Jefferson ultimately rises above thinking of himself as a hog. When Jefferson gets his notebook and starts writing down his thoughts, you can literally see the evolution in the way he sees himself. He writes, "If I ain't nothing but a hog, how come they don't knock me in the head like a hog? Starb me like a hog? More erasing, then: Man walk on two foots; hogs on four hoofs" (28.17). Jefferson is questioning the label that he has been given by society, and thinking himself as a man. Go, Jefferson!
Finally, by the time of Jefferson's execution, the hog has disappeared and only the man is left. His last words, "'Tell Nannan I walked'" (31.53), show the way that he has become a man who walks on his two feet, not a hog that crawls. And, symbolically, he's proving himself above the racist thinking that called him a hog in the first place.