What is Twain satirizing in the episode where Colonel Sherburn shoots Boggs in The Adventures of Huckleberry Finn?
As the other response to this question notes, Twain is certainly satirizing Colonel Sherburn's obsession with his personal honor. However, in addition, Twain is also satirizing men's obsession with defending the status of their own masculinity.
We can assume Sherburn is anxious to defend his status as a man based on what he says when he addresses the mob trying to lynch him for Boggs' murder (there are no page numbers for the quote below because I took the passage from eNotes' excellent online text of the novel):
“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."
Based on Sherburn's speech, it's clear that his masculinity is near and dear to his heart. His language is clearly gendered to assert that he is a "man" while the mob members are "feminine." Additionally, it's apparent that Sherburn thinks his maleness is superior to the "feminine" nature of the masses, and so he's willing to murder someone just to prove how "manly" he is. By casting the colonel in such a bombastic and exaggerated fashion, Twain satirizes men's tendency to go to extreme and ridiculous lengths to prove their own "maleness." Moreover, Twain illustrates how this tendency has violent and destructive consequences for society at large. After all, if men are going to go around shooting each other to defend their manliness, then society is doomed to a violent cycle of murder followed by angry mobs.
In my opinion, Mark Twain is satirizing the pre Civil War tendency of Southerners to be very concerned with their personal honor.
The South had evolved a society where the highest classes saw themselves as similar to the aristocrats of old Europe. They felt that their personal honor was so important that it was not at all uncommon for them to fight duels when they felt they had been insulted. This was part of the society that was responsible for slavery as well.
Twain satirizes this by having Colonel Sherburne be so jealous of his reputation that he shoots Boggs for being disrespectful.