The premise of "After Twenty Years" by O. Henry is a simple one: two young friends part ways, one stays in New York and one heads West, and agree to meet at a specific time and place twenty years later. What happens at that time and place is the crux of the story.
Bob has been out West, and he has obviously had some success. He is dressed well and has a diamond stickpin and watch. He is waiting on the corner where he and his friend Jimmy had agreed to meet, and a police officer approaches him. Concerned that the officer might think he was up to no good (which is quite ironic, given what we learn later), Bob lights a cigarette (by the light of which the officer can see the man's face more clearly) and tells him the story of why he is here.
"Twenty years ago to-night," said the man, "I dined here at 'Big Joe' Brady's with Jimmy Wells, my best chum, and the finest chap in the world. He and I were raised here in New York, just like two brothers, together. I was eighteen and Jimmy was twenty. The next morning I was to start for the West to make my fortune. You couldn't have dragged Jimmy out of New York; he thought it was the only place on earth. Well, we agreed that night that we would meet here again exactly twenty years from that date and time, no matter what our conditions might be or from what distance we might have to come. We figured that in twenty years each of us ought to have our destiny worked out and our fortunes made, whatever they were going to be."
Bob is correct; each of them has found his destiny. Bob, as it turns out, has become an infamous Chicago gangster, and Jimmy has become an upstanding policeman. While Jimmy recognizes Bob, Bob does not see the officer well enough to recognize him as his old friend Jimmy.
Now Jimmy has, it seems to me, three choices: does he arrest his childhood friend (who is now a wanted criminal), does he just walk away and pretend he never saw Bob, or does he acknowledge Bob but ignore the fact that Bob is a wanted criminal. None of the choices are good ones for Jimmy.
Clearly the twenty years that have elapsed have, as Bob said, determined his destiny. He went West and chose a life of crime. Though he is still a loyal friend to Jimmy because he showed up here tonight and is even willing to wait an extra half hour for him, Bob is not a good man or a good citizen. His choices have made him rich, but they certainly have not made him a better man.
Those same twenty years have shaped Jimmy's destiny, as well. Jimmy chose to spend his life upholding the law and, ironically, protecting others from people just like his old friend Bob. This is still not an easy choice for Jimmy, for he is also a loyal friend. Even so, Bob unknowingly reveals what Jimmy must do when he describes him this way:
"But I know Jimmy will meet me here if he's alive, for he always was the truest, staunchest old chap in the world."
So now we realize that Jimmy has no choice; because he is a trustworthy and staunch (loyal, committed, and strong) police officer, he has to arrest Bob. He manages to do the right thing while still remaining a friend to Bob, sending someone else in to make the arrest. That is the best he could offer his old friend; he spares Bob the embarrassment and indignity of having to face his old friend in handcuffs.
If I had been Jimmy, I would hope that I would have been both compassionate and moral enough to do exactly the same thing.