When an author portrays a character, he uses what he says about the character, what other characters say about him/her, and the actions and words of the character himself.
What the author says: We find out at the end of the story that Jimmy Wells is a policeman. However, O'Henry describes him in the first sentence of the story.
"The policeman on the beat moved up the avenue impressively. The impressiveness was habitual and not for show, for spectators were few." (page one)
Jimmy makes a fine impression of a police officer even though there is no one to impress. It is just the way he is, and he is not putting on airs. O'Henry also tells us that he was,
"...twirling his club with many intricate and artful movements, turning now and then to cast a watchful eye down the pacific thoroughfare" (page one)
This tells the reader that he has been at his job for a while because he has developed an art of handling his billy club. A billy club, in case you do not know, is the stick that police officers carry when they walk their territory (beat). He is also very observant. This is reinforced later in the story. O'Henry continues by telling the reader that Jimmy,
"....with is stalwart form and slight swagger, made a fine picture of a guardian of peace." (page one)
This shows Jimmy as a sturdy, robust character who looked as a policeman should look.
What other characters say about him: When Silky Bob is telling the police officer about Jimmy, he describes him as ,
"...the finest chap in the world." (page one)
"....raised here in New York." (page one)
"I was eighteen and Jimmy was twenty." (page one)
"You couldn't have dragged Jimmy out of New York; he thought it was the only place on earth." (page two)
"...he was always the truest, stauchest old chap in the world." (page two)
"He'll never forget." (page two)
"He was a kind of plodder though, good fellow as he was." (page two)
So Jimmy was two years older than Silky Bob. He had been raised in New York and loved the city. However, he did not crave the excitement that Silky Bob did, and he generally just lived day by day, taking a rather humdrum existence over the excitement that Silky Bob craved. However, he is a good friend and a fine person. If he could make the appointment, he would be there. When Silky Bob realized that the man who meets him is NOT Jimmy, he says,
"Twenty years is a long time, but not long enough to change a man's nose from a Roman to a pug." (page 3)
So we know that Jimmy has a Roman or long, straight nose.
The characters actions or words: Jimmy shows that he is observant when he write in his note to Silky Bob.
"When you struck the match to light your cigar, I saw it was the face of the man wanted in Chicago." (page 3)
He shows that he is a good friend when he writes,
"Somehow I couldn't do it myself, so I went around and got a plainclothesman to do the job." (page three)
He also shows that he is a moral, law-abiding person because he does have his friend arrested. He cannot ignore it.
Bob said that if Jimmy could be there, he would because he was a good friend,and Jimmy was there. He also says in the note.
"I was at the appointed place on time." (page three)
My copy of the story is off the internet. The pages may differ from your version. However, I have tried to put everything in order, and you should find the quotes relatively easily.
Jimmy had to make a difficult choice between two painful alternatives. On the one hand, he could have gone on his way and let Silky Bob escape from the law. In that case, Jimmy would have felt guilty for failing to do his sworn duty as a police officer. On the other hand, he could arrest Bob or cause him to be arrested. In that case he would have felt guilty for betraying his old friend.
Jimmy is not the viewpoint character of the story, but O. Henry is such a good writer that he makes us realize that Jimmy was experiencing many mixed feelings about Bob and about himself. Bob is the viewpoint character and does a lot of talking about himself. We understand that he is in a sentimental mood. He wants to see his old friend and talk about old times. He is a stranger in New York, but this city used to be his home. Jimmy's feelings are hidden, just as he himself is practically invisible throughout the story. Bob fails to recognize him because it is a fact that a uniform tends to obscure the wearer's identity. We see a cop and not the individual. This is probably the reason for uniforms, including military uniforms.
Jimmy is especially invisible in this story because the New York cops must have worn navy-blue uniforms and it was nighttime on an unlighted street. Jimmy would have blended into the darkness. Then Jimmy does not reveal himself or make the arrest personally; he passes that job on to another man. Jimmy seems like a sensitive man, judging from the note he has the other man hand to Bob. No doubt Jimmy was sorry for doing what he did, but he knew he would be equally sorry, if not sorrier, if he didn't do it. He was in a lose-lose situation. All of us have to make such choices in our lifetimes.
Jimmy had to make a decision, and he was guided by the training he had received at the police academy. He had been taught that as a police officer he could not be guided by personal feelings but that he had to uphold the law as he had sworn to do. He was taught this rule of conduct because his teachers knew that sooner or later he would need to remember it.
O. Henry rarely seemed terribly sympathetic to cops, but in this story he shows that his famous compassion for humanity includes cops along with the rest of humanity.