As a skater, she will be remembered:
*For her combination of athleticism and artistry, grace and poise, power and dominance.
*For her consistency--never finishing off the podium in her entire career, having won all the major titles she could get, and medalling at the Olympics back-to-back. She's always landed on the podium at major events even with little prior competition to prepare with.
*For her competitive mettle--she more than any other skater of her era, was able to consistently rise to the occasion, doing her very best and going clean back-to-back at Worlds and both the Vancouver and Sochi Olympics. Her ability to withstand Olympic pressure and expectations is unparalleled.
*For her magnificent toe jumps and 3/3 combinations. She has likely the most consistent 3/3 of all time, and landed the most in international competition.
*For pioneering figure skating in a country that had a very minor federation and poor training facilities, and expanding Korea's strength in winter sports beyond speed skating.
There's more to mention (such as her philanthropy), but those concern her as a person, not her skating career.
A total package. A mysterious combination of power and delicacy.
Anyone who has seen her skate live would agree with me; she skates like men. Her jumping technique and speed resemble male skaters'. Yet, she has the most feminine look on ice, like a super-model with ballerina's arms. Due to this strange combination, she was able to produce many magical performances.
I don't know what the rules about links are but I think she'll be most remembered for her mental approach. Wrote about it below:
Yuna was the first Olympic gold medalist since Oksana Baiul (1994) to win without the full set of triples (minus triple-axel), and I think that she will be the last. That alone shows that she was a skater who honed and perfected the skills that she did have, and had the ability to peak exactly at the right moment.
She was a great strategist and competitor.
I know many ubers claim that she could do a triple-loop because she did in her junior years, but she never did one in her adult years, and you have to do one in competition to claim you can do one. Mao could do quad salchow and loops in her junior years, and Miki continued to be able to do a quad salchow into her teens, after all, but you don't see posters claiming that Mao and Miki could do quads. Well, actually, Guiness Record says Miki did do a quad when she was 19-year-old, I believe.
Anyway, Yuna was a great strategist and competitor, and I think that is what she will be most remembered for.
She did triple loop in her 07-08senior season, but she didn't sucess it as consistantly as she did other 3jumps. And she will probably be the last skater who did 2 clean programs in 2 olympics.