"The girls read the books on the table."
Translation:Fetele citesc cărțile de pe masă.
I think it works like this: In Romanian, if you want to modify a noun or noun phrase (like "cărțile", "the books") with a prepositional phrase (like "pe masă", "on the table"), you need to link them with a "de". (Sometimes the "de" gets joined with the next preposition, so "de în" > "din", but that's not relevant here.)
Without the "de", you get the prepositional phrase modifying the verb instead.
"Fetele citesc cărțile de pe masă." - "The girls read the books on the table" - the books are on the table
"Fetele citesc cărțile pe masă." - "The girls read the books on the table" - they're reading on the table.
So both Romanian sentences can be translated with the same English sentence, but they have different meanings. The English sentence is ambiguous.
(If I'm wrong, please correct me! I'm still very much a learner, but that's the pattern I've put together.)
My understanding is the "de pe" indicates a movement : from . "pe" alone is a situation: "on" . You can imagine that your eyes which are reading word from the book on the table and bring them to your brain. So "de pe masă" is more indicated in this case. Like I read in another comment. "pe masă" in this sentence means , the girl is on the table and reads the book. It's also possible but means something different.