Translation:They deliver books to their pupils.
The clue is the dative object: komu dostarczają te książki? For whom are the books? Plural drive dative: swoim uczniom. Unlike English, Polish uses cases instead of prepositions (like to/for) sometimes. Polish also does use for: dla, however. This preposition takes on a different case and hence the sentence changes: dostarczają książki dla swoich uczniów. I hope this helps.
Wordreference tells me that "to deliver" can be both "doręczać" and "dostarczać". Is there a difference between them? If there is no difference, why did Duolingo decide to teach us "dostarczać"? I have nothing against that word; I'm just wondering because Wordreference mentions "doręczać" first.
Doręczyć (once)/doręczać (multiple times) means "to deliver by hand" in Polish. This type of transport relates to small items like mail, newspapers, small food orders, eg. milk, sandwiches, pizza.
Delivered by hand items may be left in the mailbox or at the door.
Some delivered by hand (doręczane) items, like important personal documents or court papers, have to be delivered to and signed by
the specific person. This type of delivery is called "do rąk własnych".
When big items (furniture, appliances) are delivered to the client's home, this type of transport is called "dostawa/dowóz/przywózka/ przywóz do domu" (home delivery).
Polish people say they buy or order things "with delivery" (z dostawą do domu") or they want the purchases to be delivered (przywiezione/ przytransportowane/dowiezione/dostawione/dostarczone do domu).
It is unlikely that schools transport books to their students, but as it
comes to the Polish sentence, it is correct, even though... strange.
The more likely meaning of the sentence is that schools deliver, that is supply, provide or are the source of books. In this meaning, the verb "dostarczają" requires genitive case (Dopełniacza kogo? czego?):
Dostarczają książek swoim uczniom - They supply/provide books... Dostarczają książki do swoich uczniów - They deliver/carry books...