What is a theme and how do I write about it in finals?

A theme is like the big takeaway from a narrative. Pick your favourite Disney movie; I really like 'Up'. In Up with the old man and the young boy getting to know each other and warming up to each other, the topic I would say is about family, and a possible theme would be something like the benefits of letting people into your heart--or you could take a cynical approach and say since the bad guy was once a role model but betrays them, the theme is about the dangers of admiration. Either way there is no right answer, as long as you can back up what you're saying.
You should do the same in finals. For a literature paper you should refer to what you see as the big moral of the story, and what made you think that. For a language paper, the theme may be less apparent than a fairytale style moral, but there is still always a takeaway. In an article for example sometimes the theme can be as simple as 'bees are important to the environment'. Whatever you feel as though the text imparted on you is the theme, and to write about it you'll need to describe and pinpoint why.