As the Context is the situation that resulted in the plot as we see it at the beginning of the story, the Backstory is the Context specific to a single character.
In its simplest form, the Backstory is simply the series of evens that happened to the character before we were introduced to them.
It's interesting to note that you can absolutely have a compelling character when the audience knows nothing of their Backstory, but you can't write a consistent and interesting character without knowing their Backstory yourself as the author.
Let's dig in.
Let's take a look at one of my favorite fictional characters of all time: Prince Zuko, from Avatar: The Last Airbender. (I would never presume to say that any series or story got everything right but DANG they did an awesome job in worldbuilding and character creation.)
In the very first episode, we're introduced to a boy who wields authority like a scythe, who has this strangely desperate desire to capture the Avatar. Before we know word one about his backstory, we can already make some guesses. As the series unfolds, rather than revealing "no, wait, it was actually this" the writers filled in the gaps in his history, providing reasons that supported how he acted and the choices he made, even when they didn't make sense at the time.
We could easily contrast him to someone whose history we know almost nothing about: Han Solo, from the Star Wars series. (I'm pulling data exclusively from Episodes IV-VI, because that's what I know best.) He is easily one of the most interesting characters out of the original three movies, but we know nothing about his family, his adolescence, how he got into smuggling - we don't even meet any of his friends until Lando is introduced, and even then we get almost nothing of his background past the point at which he was already a known smuggler.
Both of these characters have extensive backstories, but we only know one of them. Does that make the second character less appealing? Absolutely not! (I actually really like the mystery around him.)
Without the foundation of the backstory to support the character's behavior, it's likely to shift and change unpredictably, based almost exclusively off what would be narratively convenient or interesting, or only slightly better, a description of what they "should" be like.
If you've ever read a fanfiction that starts off with 2 or more paragraphs about what the main character looks and acts like, then you know what I'm talking about.
With all this in mind - how should a backstory be used?
The answer: It depends on you and your story.
Super helpful, I know. But you must keep in mind that not every story is the same, and the message you're delivering with one story might benefit from the character's history, while another wouldn't.
My advice is this:
Start off with your backstory developed, but don't write it out in-story unless the characters bring it up organically.
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