There's not really a set definition. Some would say a residential school, pretty much. Others (including me) would use the term to describe a serious ballet studio following certain guidelines regarding training (hours etc) in preparation for a professional career, most of the time with a student company attached, and who has dancers go on to professional careers following their years at the studio. Not all obviously, but regularly produces employable ballet dancers.
Soooo.... Gymnasts excelling at dance. It can happen. But it's certainly not a given. So many variables. Only in my own little world, we have now been part of two dance studios, one a serious ballet school and the other a nicely rounded dance studio (still with a good ballet program) with more other genres and which has a competition team.
My DD, now 14, switched over to the competitive dance studio almost 2 yrs ago.
At the ballet studio, we had several gymnasts try ballet for a while and none stayed except for ONE. Super sweet girl, but a ballerina she was not. She just never looked right doing it and her quality of movement was always more powerful than graceful. She did it for many years but eventually quit, I believe she is doing cheer in school now and I *think* she's doing a hip hop class on the side for fun.
As far as actual ballet, there comes a time when the way the muscles need to be developed for gymnastics become a hindrance in ballet.
My own gymmie, who has danced in several genres off and on through the years, is NOT a dancer, lol! She did ballet and hip hop at her sisters studio last year and although she could keep up just fine with the other girls (and actually was a surprisingly good hip hop dancer!!) it was still obvious to anyone watching that she was not a ballerina. Her body/musculature made it difficult for her to obtain the same movements as the other girls who had been doing ballet much longer. However she WAS in much more control of her body than the girls her age just starting out and did much better than the other beginners. There is no way I would expect her to have success on the competition team if she were to want to do that today. Perhaps in another year of dance training, and then her dance parts would likely be heavy on the acro.
Then, we have one girl who used to do gymnastics with my DD and moved over to dance a few years ago, around age 8. She is a gorgeous dancer and got out of gymnastics before getting too specialized, which I think helped her.
Now, it should be said that her "featured" parts all include acro tricks, she's not selected because of her dance qualities but rather for the wow factor of the tricks she can do (usually walk overs, spiders, scorpions etc).
Because she was reasonably young when she switched to dance, I can't really say whether she had an easier time learning dance or not. 8 isn't really a "late" start. Because of gymnastics she was certainly already stronger and more flexible than the average 8yo off the street though.
So I guess the short answer is that you can't expect a gymnast to be at THAT much of an advantage going into dance, but you can and should expect SOME advantage, if only the fact that she is flexible and in control of her body. However, at this age (10-12?) the serious dancers at a studio will likely have had many years of dance training and also be very flexible and in control of their bodies.
I would strongly suggest starting by taking classes for a year and worrying about performance/competition teams later. Get the feel for it first. Let the teachers get to know her and her strengths, let her have at least a year of solid dance training to figure out if she likes it first.
Older Dd, even coming from a high quality dance studio, waited to join the competition team. Her dance teachers WaNtEd her and actively pursued her to join. We have had other dancers who also switched over and joined the competition team right away, one was so overwhelmed that she ended up finishing the year miserably and then quit, another JUSt joined us but she is quite shell shocked at the moment.... I think she will be fine come season though.
In contrast, DD who waited is now one of the most responsible, featured dancers in her team. She was ready and the teachers knew her a bit better beforehand. This is her second year on the team and her teachers have all told her how pleased they are with her progress and how she is handling herself.
Hope all of that made sense!!
Best of luck in whatever she decides to do! Dance is such a fun activity and one that I love being involved in. I would just admonish her to go into it with an open mind and not expect to be given any special advantages because of being in gymnastics as really, the training is quite different.
Some studios simply have teams based on age groups and anyone who auditions is accepted, they just work with what they have, some studios are much more selective and have several levels of teams in each age group. 
