Henni was know for her lines, expressiveness, and smooth transitions. As I had seen commented on many videos of her routines, bars were her weakest element, but she still fared well on them. She competed in the 1992 and 1996 Olympics. She was 6 months too young to compete in Seoul in 1988, so she debuted on the Olympic stage at 18. When I saw her floor routine, I saw her weight: 77 pounds! While she was only 4'10", I was still amazed that a gymnast weighed 20 pounds less than 100, which is normal for her height considering the sport she's in. Otherwise, you see her perform a triple twist, which was an unusual tumbling pass at the time. I love seeing the twists and her music choice of "Hungarian Rhapsody" is an apt one.
She fared very well in the 1992 Barcelona Olympics: she won gold on vault (which she had to share with Miloşivici) and placed second on floor behind Miloşevici. I wish there was some epic archnemesis story to this, but Henni was way too modest to make a big deal out of her medal standings. According to the Couch Gymnast, when the International Gymnast magazine asked Henni how she felt about being the world vault champion she merely replied, "Good, but the world has not changed. I am still the same. It's a good feeling, but I am not in heaven. I am very happy life is the same and training is the same." Good on her! It takes a lot of mental toughness to not let achievements go to your head. She even retired after the '92 Olympics and went to the States to coach and get a university degree. She tried to compete in the NCAA, but timing wasn't working in her favor. She decided to make her comeback in '96 for the Atlanta Olympics.
You can find more on other Hungarian gymnasts on Couch Gymnast, which does a lovely summary. More information can be found here as well (particularly for the gymnastic enthusiast).