It's like saying "This is..." expect the word order is reversed here. You can say:
Taniec to moje hobby = Moje hobby to taniec. (to + nominative),
Taniec jest moim hobby = Moim hobby jest taniec. (jest + instrumental).
You should be already familiar with these two forms of the sentences on the left (This is... construction in Polish). I can explain it briefly if you are not.
Hm... Actually the equivalent of "Moim hobby jest taniec" would be "Taniec to moje hobby", because the object is "moim hobby" (instrumental case).
If you say it the other way round, it will sound like you just have one hobby, which is dancing. However, to be fair, this is exactly how the main English answer sounds like...