The Harlings are a family in Black Hawk that Ántonia goes to work for when she first comes to town. They provide an example of a successful, more "urban" family (compared to the farming families we meet in the first part of the novel). Mrs. Harling is an important character in that she teaches Ántonia to be more domestic and feminine. (Ántonia later reflects that these were important lessons for her to learn.)
Mr. Harling is a successful merchant, but we don't know much else about his character. The most important thing he does in the novel is forbid Ántonia to go to the dances, which allows us to see Ántonia's independent nature. The Harling children show us early on that Ántonia would make a good mother, as she enjoys taking care of them so much.