Although Mr. Underwood, the editor of the local paper, is a minor character in the book and is almost never directly quoted, his ideas are extremely significant in undertanding the events that take place in Maycomb concerning Tom Robinson. In Chapter 25, he writes about the trial that has just taken place, and Scout relates the jist of what he is saying without actually quoting his words. Scout says, that Mr. Underwood
"didn't talk about miscarriages of justice, he was writing so children could understand. Mr. Underwood simply figured it was a sin to kill cripples, be they standing, sitting, or escaping. He likened Tom's death to the senseless slaughter of songbirds by hunters and children."
After pondering upon Mr. Underwood's words for awhile, Scout comes to an understanding of what he is trying to say. Mr. Underwood means that
"Atticus had used every tool available to free men to save Tom Robinson, but in the secret courts of men's hearts Atticus had no case. Tom was a dead man the minute Mayella Ewell opened her mouth and screamed."
Despite the lack of direct quotes attributed to Mr. Underwood, he apparently is a man who can be quite garrulous. In Chapter 15, on the night that Atticus holds vigil over Tom Robinson, trying to ensure his safety by sitting in front of the jail, Scout notes that "it seemed that Atticus and Mr. Underwood would talk for the rest of the night." Just previously, a mob had come to take the law into their own hands, only to be defused by the innocent talk of Scout, who appeals successfully to their individual sense of decency. When the incident is over, Mr. Underwood comes out and says the only words directly quoted by him that I could find. Mr. Underwood, holding a double-barreled shotgun, calls out after Atticus tells Tom the men won't be bothering him anymore,
"You're damn tootin' they won't. Had you covered all the time, Atticus."
You've already gotten an excellent and thorough answer, so I'll just add my two cents.
In chapter 16, Atticus is "guarding" Tom at the jailhouse. He has no gun or other weapon, though, so he's really just there to stop whatever might occur. Mr. Underwood, on the other hand, is prepared to shoot. Once the ordeal is over and Atticus is ready to walk the kids home, he reassures Tom they're gone and they won't bother him any more.
"From a different direction, another voice cut crisply through the night: 'You're damn tootin' they won't. Had you covered all the time, Atticus.' Mr. Underwood and a double-barreled shotgun were leaning out his window above The Maycomb Tribune office."
The only other time Mr. Underwood features prominently in the novel is in right at the end of chapter 25. Tom has died, the town has gossiped, and the dust is about to settle. Then we hear Mr. Underwood's scathing editorial, where he writes "it's a sin to kill cripples, be they standing, sitting, or escaping." This mirrors (or echoes) the theme of the title and of Atticus's words--"it's a sin to kill a mockingbird."
Like so many minor characters in a novel, Mr. Underwood reflects the position of one of the major characters in the novel. His is not a grand role, but he is able to express the outrage and unfairness of this trial and its outcome which Atticus, by nature, can not speak.