What is the relationship between history and literature?
I agree that this question is extremely broad. You might want to place it on a discussion board so various people can respond to various aspects of the question. I'll contribute one aspect to possible answers.
It is important to know first of all that history is literature, too. Today scholars believe that "true" and completely accurate history does not exist. History is written by those educated enough to be able to write, as well as by those who have the leisure time to write it. For most of the western hemisphere, at least, that means the history we have today was written by a few wealthy white men. That's not at all comprehensive. Most importantly, history is written by the winners. Most of what we know concerning the battle of Hastings in 1066, for instance, comes from the victors, the Normans. Losers aren't usually around to write history.
We do learn about a society from the literature it produces, but the knowledge we learn is always fragmented and incomplete.
This is a pretty broad question, and I wonder if you might want to clarify it a little.
To me, the relationship is that literature can be a reflection of the characteristics and nature of a certain time and place in history. By reading the literature that is written at a certain time and place, it might be possible to learn something about the concerns and values of that particular moment in history.
An example of this would be "The Great Gatsby." The novel was written in the 1920s and it reflects some of the concerns that intellectuals (at least) had about the time. It shows how some people were concerned with the emptiness of American life at the time. They felt that Americans were concerned only with having a good time.
From an academic standpoint, these two subjects are closely interrelated to me. As a teacher, literature is essential in helping students understand the midset of a society, or a segment of society, in the time period of the novel. History is also a subject best taught through stories, as its name suggests. So to put the bare historical facts into a story with real characters, interactions and emotions is a powerful teaching and learning tool in today's education system.
Of Mice and Men, The Jungle, Uncle Tom's Cabin and How the Other Half Lives are all reflections of society in its historical element.
The relationship between history and literature is one based on context and provenance. The relationship works both ways. In order to understand a literary text, it is often important to understand the atmosphere in which a text was written. Understanding the context in which the author created the novel provides great insight into the characters, symbolism and morality. On the other hand, when studying history it is important to read fiction of a certain time period as well as literature created by people who lived through the period you are studying. A great example is Liam O'Flaherty's Return of the Brute, written in 1929 and based on the author's experiences in World War I. Understanding the history of World War I greatly improves the reader's understanding of the text. Studying World War I through this novel provides historical context from someone who lived through it.