The exposition of a story is information which, although not a part of the story you are writing, is nevertheless necessary to explain the events.
For the most part, though, exposition is commonly understood to mean information about a character's past (which is more commonly known as the backstory).
It fits into the definition of exposition I gave above because events from a character's past are not a part of the story being told in the here and now, but they nevertheless have a bearing on it.
So if a novel is about a woman battling cancer, for example, the fact that she was abused as a child isn't part of the cancer story but will nevertheless have a strong effect on the woman's character.
We are all a product of our pasts, and it is no different for a central character in a novel. They, too, have a history that has made them the person they are at the start of the novel.
Which means that if the reader is to get to know the character fully, and understand the events of the novel fully, they need to know about this history.
They need to know where the character has come from, what their childhood was like, why their marriage failed - anything, in fact, which helps to explain what they are doing here now, what they want, and why they want it.
The first thing to understand about handling a novel's exposition is that the reader's interest always lies with the story itself...
Exposition might be necessary to explain the events, but the events themselves - the plot, in other words - must always come first.
And so the key to handling the exposition of a story is to get in and get out fast.
In other words, present whatever facts you need to get across in as small a space as possible - a few lines of dialogue here, a small paragraph of narration there, nothing more.
One way to work in these snippets of background information is to incorporate them into the dialogue...
"Staying long?" asked the receptionist.
"Two days, maybe three," said Frank. "I've got to be back in London for my daughter's birthday."
"Family man, huh?"
"Two boys and a girl," he said. "And a wife somewhere in France sleeping with a kid half her age."
Or you can simply work them into the prose, either through the narrator telling us the facts directly, or (as in the example below) the character thinking them...
"Family man, huh?"
Frank took his key and started up the stairs. He could have told the lady that he had two boys and a girl back at home who were missing their daddy like hell, and a wife somewhere in France sleeping with a kid half her age, but he really wasn't feeling chatty right now.
However you work in these snippets of exposition, just remember to keep the information brief...
Oh, and another thing - try to keep all exposition well clear of the beginning of your novel.
Your main job when plotting the beginning of a novel is to hook the reader, and the way to do that is to get them engrossed in the story.
If you disrupt the story to talk about the character's childhood or tell the history of the town in which they live, you run the risk of losing the reader. So hold back the background facts for a chapter or two.
If the exposition of a story is handled well, the readers should be able to absorb the information without ever being aware that they are being force-fed it.
But what if you have a lot of information to get across?
What if an episode from a character's past is crucial to explaining the present, and you are just not going to be able to tell it in a few lines of dialogue?
The answer is to make a scene out of it, to turn it into a dramatized flashback.