Content is what is actually in a piece of writing (or TV show or film or whatever). Context is the circumstances under which it was written and the extra information which helps us to understand the piece of writing.
For instance, here on iTalki Answers people often ask questions and sometimes it's hard to answer because we don't know the context. I can explain the content (what the words actually mean, the grammar) but I need to know the context to give you a fuller answer. For example, who wrote it? Does the writer have a relevant background which helps us understand their meaning? When was it written? What happens before and after in the story that explains what is happening?
For instance, if I read a novel set in Romania in the 1980s I could read it (the content) and enjoy it without knowing anything about Romania in the 1980s. But if I knew about the history and politics of Romania in the 1980s I might understand it better and get more value from it - this is the context.
So in short, content is the actual words used and context is everything not in the actual words but which helps us to understand.