"Copying from a book" would be „copiind dintr-o carte”. „Copiind din carte” implies that the speaker already knows which book is meant.
In Romanian, articles (mostly definite articles) are omitted when the noun is preceded by a preposition (here: „din”). A few more examples:
Mă duc la mașină să iau cartea. - I am going to the car to take the book.
Tocmai am venit de la școală. - I have just come back from school.
Am cumpărat lemne pentru grătar. - I bought some wood for the grill. (to light the fire)
This is pretty consistent. One important exception is the preposition „cu” (with), which does not follow this pattern and is usually used with an article.