We know very little about Jim. He only appears towards the end of the story and is not given any physical description, although we can assume that he is young and good-looking enough to make Della love him. The fact that he has been carrying a gold pocket watch suggests that he works in an office and wears a suit and necktie. He is not doing very well in the world of commerce. He had been earning thirty dollars a week, but now he is only earning twenty dollars a week. A young man should be getting raises and promotions, but Jim seems to be moving down the ladder instead of up. This suggests that he is either not very ambitious or not very talented. He shouldn't have to be selling his gold pocket-watch in order to buy his wife a modest Christmas present. And she shouldn't have to be selling her precious hair to buy him a watch-chain. Della thinks that the chain she buys for her husband is like him and like his gold watch: it has "quietness and value." Maybe he is a little too quiet. He may be the kind of man who just does his job conscientiously and never gets noticed or appreciated by his superiors. The fact that he sells his treasured watch shows that he is a loving husband. We suspect that these two people have not been married long. They are still in the honeymoon stage of marriage. Della will get tired of wearing old clothes and pinching pennies. Jim will get tired of his dead-end job. Then they could easily get tired of each other. 

You already have an excellent answer by magana584, so I just have a few things to add. In O. Henry's "The Gift of the Magi," James Dillingham Young used to earn thirty dollars a week; however, he now only gets twenty dollars a week, and of course that means he and his wife, Della, must be much more careful with their money. Della loves her husband very much. Every night when he comes home she hugs him, which, the narrator says, "is all very good."

They do not have very many fine things, but one of them is Jim's gold watch. It was handed down from his father and his grandfather, and he is very proud of it. 

Had King Solomon been the janitor, with all his treasures piled up in the basement, Jim would have pulled out his watch every time he passed, just to see him pluck at his beard from envy.

When Della finds the perfect fob for Jim's precious watch, she describes it--and her husband--this way:

It was like him. Quietness and value--the description applied to both.

Della is worried about Jim's reaction when he sees that she has cut off her long, beautiful hair. She has no idea, of course, that he has bought her combs with the money he got from selling his watch. When he sees her, he is surprised, naturally, but he is not angry or upset either at her short hair or the fact that he sold his watch for something that turned out to be useless to Della. He rather sees it is a delightful joke and just wants to set both gifts "aside for awhile" and enjoy Christmas with his wife.

From all of this we can characterize Jim as a kind man who loves his wife enough to sacrifice what is most important to him for her happiness. He works hard and has a positive outlook on life; he is also optimistic about their future together. 

Jim is hard working and dedicated to his family. He doesn't get as much description in the text as Della does, but the little we see of him tells a lot. He is obviously thoughtful and caring since he sells his treasured watch to get Della an elegant set of combs. He is also described as "thin and very serious," which could be interpreted as a result of his stressful money situation. But Jim's main characteristic is that he is loving. He never complains, though he needs new clothes and is barely making ends meet, and he sacrifices his prized possession to buy Della a gift. He always "greatly hugged" his wife when he got home. At the end, he is undisturbed by Della's change in appearance and doesn't seem bothered that the he has no watch to put on the chain Della bought for him. He calmly sits on the couch and asks Della to get dinner, which likely puts her at ease.

Describe Jim's character in "The Gift of the Magi."

The middle name Dillingham plus the fact that Jim inherited his gold watch from his father who had inherited it from Jim's maternal grandfather suggest that Jim comes from a social class superior to that to which he and Della now belong. The name Dillingham in itself does not necessarily mean that Jim comes from a higher class, but the fact that O. Henry puts it in the story and emphasizes it shows the author intended to imply something--if only to explain how a man in Jim's position could come to own an expensive gold watch. Jim values his watch because it is a reminder of his ancestry. That is why he is always taking it out and looking at it. The fact that he is always pulling his watch out of his pocket suggests that there is a mathematical probability of his dropping it sooner or later. That was why men had watch fobs for pocket watches, and that it is why it occurred to Della to buy Jim a watch fob. 

Della would seem to come from a working-class background. Here is a sample of her speech:

“Cut it off and sold it,” said Della. “Don't you like me just as well, anyhow? I'm me without my hair, ain't I?”

Della not only seems to love Jim deeply, but she also seems to look up to him as to a person of a higher social class than herself. She seems to feel privileged to be married to him. He would never use the word "ain't." She wants to buy him a present that would be "worthy" of him, which could mean worthy of a man from his social background.

Jim's character seems to reflect higher social antecedents. He is quiet, reserved, polite, considerate, soft-spoken. Della loves him for being a gentleman as well as for other reasons. 

Jim's character is a bit more difficult to describe than Della's character.  The reason for that is because he is in the story for less time than Della.  Regardless, there are some things about Jim that the story makes clear.  First, Jim is young.  The story says that he is twenty-two years old.  He's obviously married.  He has a job, but the reader is not told exactly what his line of work is.  Presumably it is some kind of job that would allow him to wear a pocket watch and not be out of place.  I figure that it is some kind of clerical job vs. a factory job.  Jim is also a calm and quiet individual.  He doesn't get angry or accusatory when he comes home and sees Della's cut hair.  Despite his meager income, he seems like a fairly positive man as well, because he doesn't come home in a depressed huff.  Instead, what is clear is that he deeply loves Della--so much, in fact, that he sold his most valuable possession in order to buy her the combs that she had been wanting.  She is the light of his existence.  

“I want you to understand me, Dell,” he said. “Nothing like a haircut could make me love you any less."

James Dillingham Young is twenty-two years old. He is a hard worker, quiet by nature, and very devoted to his wife, Della. He is employed at a job of some sort in a large city - while no specific details are given, it might be some sort of office work where he would have had reason to wear his family heirloom pocket watch, particularly if it was securely held in place with "a platinum fob chain...properly proclaiming its value by substance alone". Jim's income has been reduced, however, from $30.00 per week down to $20.00 per week, an amount that has required Jim to find a creative new way of raising enough money to purchase a Christmas present that is an appropriate expression of his love for Della.

What does Jim's gift in "The Gift of the Magi" reveal about his character?

Jim sells the gold watch, which O. Henry indicates was his "prized possession", in order to buy Della tortoise shell combs for her hair. His Christmas present shows that he is generous, even to the point of self sacrifice. He's a man who doesn't dwell on material objects. He readily gives up his watch just to make his wife happy. She is the most important thing in his life. He also seems to be a level-headed young man who takes things in stride. While he is slightly taken aback by Della's new hairstyle, he accepts it without negative comment and O. Henry reports that he was neither shocked nor surprised, as Della feared. He simply hugs Della and in this act shows the unqualified love he has for his wife. He tells her that they will put away their presents for now and use them at some future time. This shows a very sensible man who, despite the current financial situation he and Della find themselves in, knows things will get better in the future as long as he has Della's love. While O. Henry says that Jim and Della were "two foolish children" he strongly suggests that the strength of their love and willingness to sacrifice for the other makes them as wise as the Magi who brought presents to the baby Jesus so many Christmases ago.