"What movie is this?"
Translation:이것은 무슨 영화입니까?
Questions in Korean (and in many other languages) are often structured the same way as the answer is. The answer here would be 이것은 (movie name)입니다. So the question is then structured 이것은 무슨 영화입니까? where the name of the movie is replaced with 무슨 영화 and the verb ends with -까 instead of -다 since this is a question.
I know 어떤 is "what kind", so I think that would change the meaning slightly. This 무슨 is the type of "what" that we use in English when it means what/which and comes before a noun. You're trying to figure out the unknown movie, not what kind/genre of movie it is (which you might ask even if you know the title).
It's because "what" in this case is a determiner for the noun phrase "what movie" rather than a noun like in the question "what is this?".
What movie is this? -> 무슨 영화입니까?
What is this? -> 무엇입니까? or simply 뭐에요?
See the comment here for more info on the different what's: https://forum.duolingo.com/comment/24448032