The sentence is an ellipsis for "Barnen är ute och barnen leker", meaning "The children are outside and the children are playing". The English translation preferred by Duolingo compresses this further by using what in Latin grammar would be called "participium coniunctum" (Don't know what it's called in English grammar): The main sentence is "The children are out", and then a participle clause is added that relates to the subject and adds another propositional content to the sentence that relates to the main proposition in a way that the recipient has to figure out from context. In this case, the context implies than the conjunction between the two propositions is an "and" or possibly a "while". That being said, in a sentence with different message (such as this very sentence), the conjunction linking the participial construction to the main sentence could even be an "although". (Note, however, that the previous sentence does not use "participium coniunctum", but rather something I would call "ablativus absolutus" if English would use ablatives. The difference is that the participle clause has its own subject different from the main clause's.) I'm reasoning from my understanding of Latin here, but according to my English sprachgefühl the basic logic is the same in both languages.
Edit: I found something about this topic in Google books: "Free Adjuncts and Absolutes in English", https://books.google.de/books?id=ze0DAQAAQBAJ
That certainly makes a lot of sense. Now, the additional question is how typical is it for Swedish to contract sentences less than English in this manner? Does this sentence construction hold true for all/most similar sentences or can we sometimes get away with "participium coniunctum" på svenska också?
I haven't seen a single Swedish PC construction in the Duolingo course (but that's almost all the Swedish I know). Except perhaps something like "Han kom simmande": "He came swimming", corresponding to something similar to "He came in that he swam" ("in that" isn't entirely right, but English does not really have a conjunction for this and uses "by"+...ing instead. In German one would use "indem"). But I suspect this is idiomatic and works only with "komma" and a few other verbs. Better ask a Swede!
So much esoteric Latin grammar makes my head spin. :-) Seriously, I still am not sure if "The children are outside playing." or the equally typical statement, "The children are playing outside." are valid translations or if the "and" construction comes up in other Swedish sentences we should know about. Tack så mycket.
Both sentences mean pretty much the same thing in English, with only a difference in emphasis. the first sentence emphasizes that the children are outside while the second on the fact that they are playing. In Swedish, this difference is more pronounced, so the first one is a better translation, if you had to choose. The children are playing outside' in swedish would be simply 'Barnen leker ute'. there's also a short film by this name, translated as 'Kids Play Outside'. 'Barnen (ar/ verb) .... och .....(verb) ', is kind of an idiomatic construct in Swedish which is hard to translate. hope this helps.