To prepare for the next monthly exam, our teacher wrote a sample essay that included this sentence:
Sport is to our life what exercise is to our body.
But the teacher herself cannot explain the structure of this sentence :(
Is it correct? I think
(What sport is (to our life) ) is (what exercise is (to our body) ).
is the correct expression.
The simple answer is yes, "A is to B what C is to D" is a common and natural structure.
It means A's relationship to B is the same as C's relationship to D.
So, for example, if you know that A is B's daughter, then you also know that C is D's daughter.
Or if you want to express to a soccer fan that Wayne Gretzky is the greatest hockey player of all time, you might say, Gretzky is to hockey what Messi is to soccer.
So about your example sentence, I think the words are poetic nonsense, but a clearer way to say the same thing is:
Sport has the same role in our lives that exercise has for our body.
