How do they refer in English to those clubs, in which people are dancing to music with the purpose of dropping some weight? Is the word "shaping" common in that sense? Could those clubs be called "shaping clubs" or are there some better terms for that?
(I don't mean fitness centers, in which people do physical exercises instead of dancing to music)
(Body) shaping is a type of aerobic exercise, however, its association to dance is loose, at best. So I don't think that is the correct term.
The best general suggestion that I can make is to call it a dance fitness class. Google it, and you'll find plenty of places offering it. It's a very literal term, so it may not be what you're looking for.
Zumba is a very popular type of dance fitness class. It may be popular enough that you could use it in place of "dance fitness class," and your audience would understand the gist of it, even if it wasn't actually Zumba. Barre is another, but it is focused on ballet dancing. There are plenty of other general categories and proprietary names for specific dance fitness classes, with varying degrees of popularity, such as pole dancing, Jazzercise, and Bhangra.
