Jack Maldon is Annie Strong's cousin. He's a fairly useless guy. He can't hold down a job on his own, but he feels totally entitled to one. So, he expects Annie Strong to make her doting husband employ him. And because Doctor Strong is so sweet, he does: first, he hires Jack Maldon to be his secretary (which Jack Maldon is much too disorganized to do effectively). And then, when that doesn't work, Doctor Strong asks his business manager, Mr. Wickfield, to get find Jack Maldon a job.
Mr. Wickfield thinks that Doctor Strong is trying to get Jack Maldon out of the country because he suspects hanky-panky between Jack and Annie. Doctor Strong actually suspects nothing of the kind, but Mr. Wickfield ships Jack Maldon off to a post in India anyway. Once in India, Jack Maldon whines and protests about the climate so much that Doctor Strong brings him back to England, once more unemployed. Mostly, what Jack Maldon seems to like to do is to go out with Annie to the opera or whatever, all on Doctor Strong's dime.
Annie and Jack Maldon were really close when they were kids. Once they grow up, she starts to find his company tedious. Even so, Jack Maldon stays really attached to her: the night that he is scheduled to leave for India to start his new job, Jack Maldon steals one of Annie's ribbons as a memento. Annie knows that the world suspects she is having an affair with her cousin, but the world is totally wrong. Annie mostly views Jack Maldon as a nuisance and a social butterfly.
One of the most damning pieces of evidence for Jack Maldon's overall poor quality as a human being happens one morning when Doctor Strong asks him the news in David's company. Jack Maldon answers that there is no news: "There's an account about people being hungry and discontented down in the North, but they are always being hungry and discontented somewhere" (36.39).
David takes Jack Maldon's total indifference to the suffering of others to be a fashionable pose. He's not too impressed by the fact that it's cool to seem unmoved by other people's pain. Seriously, if there's one lesson we can learn from this book, it's that Dickens wants us all to feel bad for others, and any character who doesn't must have something wrong with them.