Princess Yue is the daughter of Chief Arnook of the Northern Water Tribe. She's usually seen sailing through the city in a boat with a servant/helper who takes care of the rowing (via waterbending). She recently turned 16, making her "marrying age" according to her father/Tribe traditions, which helps explain why she is already engaged. However she doesn't seem very happy about it, and even breaks into tears when Katara talks about her Gran-Gran's arranged marriage.
Princess Yue is polite and well mannered, and seems to be a kind person. She falls for Sokka soon after they meet during a banquet for the Avatar's arrival, as well as for her turning 16. While they meet a few times late at night on a bridge, she sends him a lot of mixed messages as one moment she likes him, but then the next she can't be with him. It's not until later that she tells Sokka of her engagement, but not before kissing him.
Her fiancé, Hahn, is a "self-absorbed weasel" as Sokka puts it, and cares more about the points he gains with Chief Arnook than being with Princess Yue. Well aware of the political dynamics of his culture, Hahn is a bit full of himself and is mostly concerned with pushing himself forward in his tribe. He is not a waterbender, but he is a somewhat respected warrior (I guess), considering he leads a secret attack on the Fire Navy's commanding officer when they attack the North Pole. He also cannot remember how to correctly pronounce Admiral Zhao's name (he usually calls him 'Admrial Choi'). Hahn's attack on Zhao ends pathetically, though with Hahn's ego, I doubt he'll be humbled by it and will probably make up some excuse as to why he failed.