Shane is what we call a "stock character."  A stock character is a character that is immediately recognizable to a reader, like the "mad scientist" or "lovesick young man," for example.  Shane is the quintessential loner, a mysterious gunfighter who is trying to make things right and "live down his violent past" (eNotes).  He joines forces with Joe, the narrator's father, to battle the land-hungry "land baron" (eNotes).  Shane represents all that is honorable in American society because he wants to right wrongs and is willing to give his life to fight for what is right.  The narrator looks up to both Shane and his father, because both men "share common qualities of fortitude, courage, and a determination to stand up for what is right" (eNotes).

How does Shane represent honor in American society?

I agree that Shane represents many honorable things, but we cannot forget that he is a gunslinger--a hired gun. We know that because he knows exactly what kind of man Stark Wilson is and how to defeat him, which he does. While Shane's past is probably not what most people would call honorable, what he does while he is staying in the valley with he Starretts is the epitome of honorable. He kind of loves Marian but would never act on those emotions because of his love for Joe. He does not allow the bullies (Fletcher and his men) to win the battle with the hardworking homesteaders, and he works hard without asking for much in return. Shane seems to understand that boys need heroes and does his best to preserve that image for Bob, even in rather violent circumstances. Shane would not call himself honorable, I suspect, but there are many honorable things about how he lives his life while in the valley. 

Shane is honorable, especially in the eyes of Americans, because he stands up for the underdog.  Being that America's roots come from that of an underdog, Shane does represent all that is honorable in America.  He is an honest, loyal man who cares about doing what is right.  He is willing to make sacrifices for the cause, even if it is not always in his own best interest to do so.  Shane doesn't look for violence, but he is not afraid to use violence if he has to.  Most of all, he's effective.  He's in control of the situation at all time and stays cool in the presense of danger.  In the end, he restores justice to an unlawful area.  He is a hero who is actually too unbelievable, such as heroes from tall tales such as Paul Bunyan whom Americans have come to connect with and idolize.

Well, I would disagree that he does, but I can see why you might say so. He's a very honorable character, and he represents many traditional American qualities. He's a loner, and Americans value independence. He's brave, and Americans traditionally admire brave men. He puts aside his independence to fight for a good cause, as did so many American soldiers in World War II. He doesn't seek violence, but he's willing to engage in it when the cause calls for it. And he's good at it: he is a skilled warrior, and an honest man.