Translation:Before the children drink the juice they eat a steak.
inversion (pretty important notion)
The rule is (let's see if a native dane correct me :D ) that the first part of the sentence "Før børnene drikker saften" indicate a time, it's called adverbier - group of words acting like an adverb. Having an adverb in the first place of the sentence, the subject is backboned to the 3th place, the verb being always in 2nd.
That also place an emphasis on this action/stuff. So it's important to do something before they drink juice. What is used as adverb in this place is always important (it can be time expression, localisation...)