In her death bed, Mother Abagail tells the Free Zone Committee that the only way to defeat Randall Flagg is for Stuart, Glen, Ralph and Larry to walk all the way to Las Vegas.
Once they (three of the four men) get there, they don't do anything much of consequence and
Flagg himself ends up detonating the A-bomb and killing everyone in the west.
So the question is, why exactly did the four men have to go there? What did they achieve?
To quote Wikipedia, the chain of events was:
Flagg gathers his entire collective to witness the execution of Brentner and Underwood. Moments before they are to be killed, the Trashcan Man arrives with a stolen nuclear warhead. Flagg conjures a magical ball of energy in an attempt to silence a dissenter, but it is transformed into a giant glowing hand—"The Hand of God"—which detonates the bomb, destroying Las Vegas and killing all of Flagg's followers...
So by going there, the men achieved:
If all the followers weren't there, some would probably have survived. If Flagg hadn't been angrily executing somebody with a ball of energy, there'd have been no trigger for the nuke. These are two things that the men who walked to Las Vegas contributed.
Granted, the nuke showing up at just the right moment, and Flagg's weapon getting redirected by divine intervention, are outside the effects of the two men, but - if you assume some divine inspiration to Mother Abigail's direction - not unconnected.
The particular men who went were the remaining men from the Free Zone committee. In that role, they had already shown their willingness to sacrifice for the community. So - again, assuming divine inspiration - their trek to Las Vegas takes on the role of (self-)sacrifice, in the traditional sense. To the question in the comments "Were these men special or could anyone have gone?" I would answer that their willingness to sacrifice themselves to likely torture and death is what made them special; others could have done it, but also would have been more likely to falter and fail.
I've always thought Stu Redman going had an Abraham/Isaac overtone to it, where his willingness to sacrifice his newfound happiness was required before he could be spared.
Just finished reading The Stand last night, actually. I thought a lot about this as well, and at first it really confused me. There is a line by Stu at the end that says that God was perhaps using them as a sacrifice, but Mother Abagail explicitly states that they must go West to defeat Randall Flagg.
In addition to gowenfawr's answer, I believe Larry, Glen, Ralph and Stu's purpose for going West was to divert attention away from the Trashcan Man and the nuke. Stephen King has stated before that The Stand takes inspiration from The Lord of the Rings, and at the conclusion of that series, we see Aragorn and the other good guys make a final stand at the Black Gate to divert Sauron's focus from Frodo and Sam, who were carrying the One Ring through Mordor.
This is very similar, at least thematically, to what Larry and Ralph are doing at the climax of The Stand. While they are seemingly doing nothing of consequence, in truth, they are assembling all the inhabitants of Las Vegas into one place, causing the Hand of God to form, and at the same time distracting RF and all his followers from spotting the Trashcan Man, who is taking an A-bomb into the heart of "Mordor" or Las Vegas.
I believe SK has stated that Trash is supposed to represent a Gollum-like character, so it makes complete sense that Trash destroys Las Vegas unwittingly just as Gollum unwittingly destroys the Ring. The parallels to TLotR in The Stand are great once you look into them.
