One simple way to understand the French expression "danse académie pour de ballet" is to break it down and translate all the lexical items it is made up of in English. Note that this technique has several shortcomings. For instance, it would not work when you try it with idiomatic and figurative expressions in a language. Nevertheless, it will work in this case.
The word "danse" in French means "dance" in English. Similarly, "académie" means academy, which is a place or institution where you study or get training in a particular field. Note that both these words are cognates. Next, "pour de" is a French preposition, which, in meaning, is close to the preposition "for" in English. And, as we know, "ballet" is a specialized form of dance, which is usually learnt by practice and training from experts.
"Danse académie pour de ballet," refers to a dance academy that specializes in imparting training for ballet dancing.