"I am throwing apples into the box."
Translation:Я бросаю яблоки в коробку.
Ah, Russian grammatical cases - the reason it's good to be a native speaker! :)
I put/am putting something in the box = Я кладу что-то в коробку.
If you were a native speaker, you would think like this: "I'm putting something (into whom? / into what?)..." = "Я кладу что-то (в кого? / во что?)..." Since кого?/что? are the questions we use with the accusative case, the noun will be changed accordingly -- "в коробку".
Something is (lying) in the box = Что-то лежит в коробке.
If you were a native speaker, you would think like this: "Something is (in whom? / in what?)..." = "Что-то лежит в (в ком? / в чём?)..." Since о ком?/о чём? [or в ком?/в чём?] are the questions we use with the prepositional case, the noun will be changed accordingly -- "в коробке".
I am sorry if this explanation is confusing: I don't know how to teach grammatical cases to aspiring Russian language learners. If you search for "падежи и предлоги в русском языке" (cases and prepositions in Russian), you'll come across some useful materials. E.g., here is a table of questions, endings, and prepositions for conjugating Russian nouns (I had a similar table back in my elementary school):
The image came from the following forum: http://www.bolshoyvopros.ru/questions/817179-tablica-padezhej-russkogo-jazyka-chto-takoe-padezh-v-russkom-jazyke.html
YouTube also has a lot of good material where educators attempt to explain this difficult part of Russian language in different ways. Give it a try and see if one of the explanations works for you better than others.
Yes, I think that's it. в + prepositional is something inside something else. в + accusative is something moving towards/into something else. So in this case в коробке would mean that you are inside the box throwing something, while в коробку means you are outside the box throwing something towards/into the box. At least that's my understanding :)