You can say "yiyor musun" too, both are valid. But they have different meanings. When you are making a yes-or-no question with "mi," you choose which word to associate it with and that word becomes the focus of the question. Whichever word you add "mi" after, it is like saying "or is it the opposite of this." So, in this example:
"Sen elmayı yiyor musun?" = "Are you eating the apple? [Or are you not eating?]"
"Elmayı sen mi yiyorsun?" = "Are you eating the apple? [Or is someone else?]"
In English you express this with the rhythm of how you say the sentence out loud. If you try saying it out loud with the first intended meaning and then again with the second intended meaning, you will hear that the second time the pitch changes a little to lean on "you." "Mi" performs the same function in Turkish.
Does anyone know if elmayı must mean "the apple" in this case or if it could also mean "an apple"? I.e., elmayı is apple in the accusative case - does that strictly imply determination, since being undetermined would require "bir"? Or is there any other form of the accusative ending that implies something else than determined?
I've been thinking over this sentence and I have the feeling that the English equivalent would be kind of "(and you?) are you eating the apple?". For example, you are talking on the phone with a group of friends and some of them are telling you that, by coincidence, they all carried an apple and at the moment they are eating it. And then you start to talk to another friend and want to know if he is also eating an apple. Your focus is not in the action of eating or in the object that is being eaten; what you want to know is if "he", as well, is doing whatever the others are doing. Does it have any sense?