Uncle Jimmy, Aunt Alexandra's husband, is part of the story's "background" characters -- that is to say, he never really appears, but we hear mention of him and his personality throughout the book, and Scout's opinion is none too high regarding him.
His only words to her in the past have been of a corrective or near-disciplinary nature ("Get off the fence"), and when he doesn't show up with Aunt Alexandra to stay with Atticus and family, his wife shows no great remorse.
As Scout put it, Uncle Jimmy present or absent made no difference (paraphrase). When Alexandra is asked if she will miss him, she shirks off the question by simply ignoring it. The reader is led to infer all kinds of things about Uncle Jimmy: He could just be insensitive, but we might also speculate that perhaps he goes beyond being emotionally cold, which is why Aunt Alexandra does not miss his presence.
Scout describes Uncle Jimmy as a man who "never spoke a word to me in my life except to say, 'Get off the fence'". When Aunt Alexandra comes to stay and Scout asks her of her husband, "Won't you miss him?", she ignored the question, and Scout concluded that "Uncle Jimmy present or Uncle Jimmy absent made not much difference, he never said anything." From these descriptions we can infer that he is a silent, almost non-character in the book, just kind-of there, hovering in the background. He and Alexandra aren't necessarily super close, because their only child, Scout says, was the result of a "burst of friendliness" between the two, and Alexandra was able to come and live for a long time in town.
Scout isn't necessarily a completely trustworthy narrator however; there may be more to Uncle Jimmy than she lets on. With a one-sided narrator such as Scout, we have to take her observations as just that: one-sided and perhaps tinged with her perspective.