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Knowing something about your characters past will help you understand why they are responding to situations the way they do. Think about it: your personality and prior experiences determine your actions, and from the outside they may appear surprising and unexpected.
This is what you want in fiction — to surprise the reader with something they didn’t see coming, but upon learning more about the character it all makes sense.
BTW, you don’t have to know this stuff beforehand; once you start writing the characters will often tell you who they are as you go along. But if you already know their past, it’s easier to weave into the story from the beginning.