Butch is a boxer with a fading career, who agrees to take a dive for a big payout.
We get a little backstory on him, a flashback to a day when a soldier from his dad's POW camp gave him his great-grandfather's gold watch that his father hid for years in order to pass it down to Butch. The flashback doesn't really shed any light on Butch's character, but it sets up a plot line for later in the film: we know that Butch treasures that watch.
Movie magic, people.
When we first meet Butch, he's having a chat with Marsellus Wallace, who's telling him to bury his pride and take the money for the fixed fight. Butch agrees, but has no intention of throwing the fight. Instead, he takes the money and bets on himself, planning to KO his opponent and leave town with his winnings ASAP.
Man of Few Words
Butch isn't a chatterbox like some of the other Pulp Fictioners. He's got that noir-ish terse, hard-boiled dialogue. For example:
ESMARELDA: What is your name?
ESMARELDA:: What does it mean?
BUTCH: I'm American, honey. Our names don't mean s***.
Up to this point, Butch is a movie cliché.
Butch seems to be tired of people thinking of him as a meathead who only knows how to punch things. When Vincent runs into Butch at the bar, he calls him Palooka (a derogatory term for a boxer, after a boxer in an old comic strip) and "Punchy." Butch just glares at Vincent and watches Marsellus welcome him and call him over. No love lost between those two. You can tell that Butch resents seeing Marsellus treat Vincent with respect while he's just asked Butch to swallow his pride and lose a fight. In fact, Tarantino confirmed it was Butch who keyed Vincent's car, probably because of being called a Palooka.
As Butch is getting ready to leave town with his girlfriend, he goes back to his apartment to retrieve his father's treasured gold watch, which Fabienne had forgotten to bring with her. He thinks the apartment's empty, even though he knows Marsellus must be looking for him. Then he sees a gun on the counter and hears someone in the bathroom—it's Vincent. He guns him down as he comes out of the bathroom.
He's glad to have the upper hand for a change:
BUTCH: That's how you're gonna beat 'em, Butch. They keep underestimating you.
The upper hand doesn't last very long, though. He ends up unconscious and tied up in a pawn shop basement.
Like ya do.
Do the Right Thing
Butch's shot at redemption comes after he and Marsellus have been taken prisoner and assaulted by the demented hillbilly duo in the pawn shop. He manages to escape his bonds and is on his way out the door when he hears Marsellus being raped. He can't let that continue. In his finest moment, he kills Maynard with a Japanese sword and frees Marsellus, who dispatches the other guy. But he's still worried about having double-crossed Marsellus and has to clear that up:
BUTCH: So we cool?
MARSELLUS: Yeah, we cool. Two things. Don't tell nobody about this. This s*** is between me, you, and Mr. Soon-To-Be-Living-The-Rest-of-His-Short-Ass-Life-In-Agonizing-Pain Rapist here. It ain't nobody else's business. Two: you leave town tonight, right now. And when you're gone, you stay gone, or you be gone. You lost all your L.A. privileges. Deal?
So why does Butch save Marsellus, who's been hunting him down after the double-cross? It's a matter of honor: he has to do the right things despite what's gone down before. Choosing the samurai sword emphasizes the "honor" angle in the scene—the samurai were famous for their strict code of honor.
There is also a clue to why Butch saves Marsellus, in the flashback scene with Christopher Walken's Captain Koons, and the young Butch. In the scene, Koons is relating his imprisonment with Butch's father, and tells Butch "Hopefully, you'll never have to experience this yourself, but when two men are in a situation like me and your dad were, for as long as we were, you take on certain responsibilities of the other". It's possible that these words came to Butch's mind as he was attempting to leave the pawn shop. (Source)
Tarantino never writes something into a conversation without a reason, right? Koons' talk sets up the rescue of Marsellus.
Jelly Beans and Sugar Pops
Butch does the right thing with Fabienne, too. He's a rough guy, but we see a different side of him with Fabienne. She's not what you'd expect his girlfriend to be, and he's different with her. He turns into a lovesick softie. He still loses his temper, but he's affectionate and tender. He says things like "Sweet dreams, jelly bean." He calls her "sugar pop." Anytime he sees he's upset her, he manages to calm himself down—a real feat for a guy who's just killed his opponent in a boxing ring. He's protective of her:
BUTCH: Honey, we gotta hit the f***in' road!
(Fabienne starts to cry.)
BUTCH: I'm sorry, baby-love.
FABIENNE: (crying) You were gone so long, I started to think dreadful thoughts.
BUTCH: I'm sorry I worried you, sweetie. Everything's fine. Hey, how was breakfast?
After settling the score with Marsellus, Butch goes back to the motel, picks up Fabienne on Zed's motorcycle, and heads off into the sunset in true western-movie fashion.
In case we miss the point, the name on the motorcycle is "Grace." Butch has found it, and escapes with his life.