"I like the apple."
Translation:Ich mag den Apfel.
accusativ is the word you get when you ask the question: who/what subject + noun. So in the sentence mary eats an apple. what eats mary? an apple, thus apple is the accusativ. Another way of remembering is that its the object that is something done to by the subject. I hope this helps
I can't explain cases. I'm not a linguist and never learned anything like it in school. Here is a good article though that might help. If you let us know what your first language is, maybe someone that speaks it can explain it to you. Hope this helps!
*Edit - This second link might help more because you might be able to find your first language in the menu and translate it.