Sherburn and Boggs are only in the story for a short time, and neither has anything to do with the overall plot of the novel. What gives, Mr. Twain? Well, we think they illustrate two common types of men in the antebellum South.
First, there's Boggs. He's the town drunk, and though he's belligerent, everyone in the town believes him to be 100% harmless. As one of the townspeople says, "He don't mean nothing; he's always a-carryin' on like that when he's drunk. He's the best naturedest old fool in Arkansaw—never hurt nobody, drunk nor sober" (21.40). Evidently he rumbles into town every once in a while and picks somebody to threaten. On this particular trip he's chosen Colonel Sherburn—oops.
Sherburn doesn't entertain Boggs's drunken lectures, and ends up shooting Boggs dead. The bystanders form a mob and migrate over to Sherburn's house, in attempt to lynch him. But Sherburn calmly faces them, and delivers the most articulate speech of the novel. Here's how it starts:
The idea of you lynching anybody! It's amusing. The idea of you thinking you had pluck enough to lynch a man! Because you're brave enough to tar and feather poor friendless cast-out women that come along here, did that make you think you had grit enough to lay your hands on a man? Why, a man's safe in the hands of ten thousand of your kind—as long as it's daytime and you're not behind him. (22.6)
It goes on from there—you should really read the whole thing. Basically, he's undermining the whole myth of Southern bravery. So why did Twain decide to include this speech in the novel? Was this a speech Twain himself felt like making? Is Sherburn supposed to represent a true Southern gentleman of honor, while most of the population has devolved into embarrassing riffraff?