It tells you a couple of things about Bob.
1. He really considered Jimmy Wells a good friend. He describes Jimmy as "my best chum and the finest chap in the world." He treasured their friendship, and although they did not continue to communicate in the last twenty years, he still wanted to continue that friendship. Heck, he traveled a thousand miles to make this appointment. He remembered the promise, which is a good indication of how important it was to him. Jimmy remembered the promise too. Their friendship was very strong.
2. He wanted Jimmy to see how well he had done. The two of them took different paths in life. Jimmy stayed in New York, and Bob went out to "make my fortune" in the West. He wanted Jimmy to see how successful he was now. He was nicely dressed, his "scarf pin was a large diamond", and he pulled out a watch that had the lid set in diamonds. They had made the agreement to meet twenty years later because,
"We figured that in twenty years each of us ought to have our destiny worked out and fortunes made, whatever they were going to be." (Internet copy pg 2)
He does not really believe that Jimmy did better than he did. He has trapsed all over the West making his money, and he tells the officer that,
"He (Jimmy) was kind of a plodder, though good fellow as he was. I've had to compete with some of the sharpest wits going to get my pile. A man gets in a groove in New York. It takes the West to put a razor-edge on him" (Internet copy pg 2)
Later, when he thinks he meets Jimmy, the men walk arm and arm up the street. O'Henry tells us,
"The man from the West (Bob), his egoism enlarged by success, was beginning to outline the history of his career."
So, Bob came to see an old friend, see what happened to him, and brag about his own accomplishments. Like any reunion, he wanted Jimmy to see how successful he is. My question is: would he have shown up if he hadn't been successful?
The fact that "Silky" Bob traveled a thousand miles to meet his old friend Jimmy Wells suggests many things about him. For one thing, it suggests that he doesn't have many friends, if any. Bob has been on the go, or on the run, for most of the past twenty years. His nickname of "Silky" and his air of supreme self-confidence suggest that he has made his fortune as some kind of confidence man or swindler. Such a man would have to keep moving from place to place, both to evade the law and to avoid running into his victims. He may have made a lot of enemies, but it is unlikely that he made any friends. Chances are that he never got married. He looks successful, but he may not feel like a big success. He may not have been planning to go to New York during all the years since he and Jimmy agreed to meet again after twenty years. The thought may have only recently occurred to him when he was staying in some lonely hotel room, drinking bourbon, smoking cigars, and reviewing his past life. He may have started thinking about his old friend and feeling nostalgic. He would have been approaching the age of forty, which is a turning point in most men's lives; they realize they are no longer young but have entered that rather bleak period of middle age when men start to wonder, "What's it all about?" Bob seems somewhat sentimental, but he may be sentimental only because he has missed so much in life--the very things that his old friend Jimmy has acquired, including home, family, friends, meaningful employment, a sense of belonging. Bob may have wanted to show Jimmy how successful he had been, but only in the hope of getting some assurance of that success from his friend.
If Bob was a wanted man in Chicago, he may have decided that it would be a good idea to move to a different city. After twenty years he wouldn't know a soul in New York except for Jimmy Wells. He may have been keeping the appointment because he was going to be in New York anyway and not because he was so fond of his friend that he was willing to travel a thousand miles just to have dinner with him. If Bob wanted to hide from the police he would naturally choose a big city to get lost in. It is ironic that he was such a successful crook that the Chicago police would want to track him all the way to New York. But the most ironic thing in this story full of ironies is that Bob was running straight into the arms of the law. He was literally walking arm in arm with a plain clothes policeman when he was informed that he was under arrest.